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E6

'''E6''', '''E06''', '''E.VI''' or '''E-6''' may refer to topics in science and technology, transport, music, geography, sports, and the military.

Science and technology

Mathematics

In mathematics, E_6 denotes an exceptional simple Lie group (or its Lie algebra) of rank 6 and dimension 78, belonging to the Cartan series of exceptional Lie algebras alongside G_2, F_4, E_7, and E_8.^[1] This structure is semisimple and has no nontrivial ideals, making it a fundamental object in the representation theory of Lie groups. The associated root system of E_6 is irreducible and simply laced, consisting of 72 roots (36 positive and 36 negative) in an 8-dimensional Euclidean space, with the roots spanning a 6-dimensional subspace orthogonal to two fixed vectors.^[2] The Weyl group of E_6, generated by reflections across the hyperplanes perpendicular to the roots, is a finite group of order 51,840, isomorphic to the orthogonal group O_6^-(\mathbb{F}_2) and acting faithfully on the weight lattice.^[3] The classification of E_6 emerged from Élie Cartan's systematic study of simple Lie algebras over the complex numbers, completed in his 1913 thesis and refined in subsequent works by 1914, where he identified the exceptional types beyond the classical series A_n, B_n, C_n, and D_n.^[4] Cartan's approach relied on the Killing-Cartan form and the structure of Cartan subalgebras, revealing E_6 as one of five exceptional algebras distinguished by their Dynkin diagrams—a characteristic feature being the extended arm in the E_6 diagram compared to E_7 and E_8. This classification, later corroborated by Wilhelm Killing's earlier but less complete work, underpins the uniform treatment of semisimple Lie algebras via root systems and has influenced developments in algebraic groups and representation theory.^[5] Key representations of E_6 include its fundamental ones, notably the minuscule 27-dimensional representation, which is irreducible and plays a central role in embedding E_6 into larger structures like E_7.^[6] This representation arises from the highest weight corresponding to the end node of the Dynkin diagram and admits a geometric realization via the exceptional Jordan algebra of $3 \times 3 Hermitian matrices over the octonions. In algebraic geometry, the E_6 root lattice embeds naturally into the Picard group of del Pezzo surfaces of degree 3 (cubic surfaces in \mathbb{P}^3), where the 27 lines on a smooth cubic surface correspond to the weights of the 27-dimensional representation, and the orthogonal complement to the anticanonical class forms the E_6 root lattice, encoding the configuration of exceptional curves.^[7] This connection highlights E_6's role in classifying singularities and moduli spaces of surfaces. E_6 also appears briefly in physics as a gauge group in certain grand unified theories.^[8]

Engineering

The E6 series represents a coarse subdivision in the E series of preferred numbers, featuring six approximate values per logarithmic decade: 1.0, 1.5, 2.2, 3.3, 4.7, and 6.8, each multiplied by successive powers of 10 to cover the full range of component values.^[9] These standardized values are widely applied in the design and manufacturing of passive electronic components, such as resistors, capacitors, and inductors, to streamline production processes, reduce inventory complexity, and ensure interchangeability among suppliers.^[10] By limiting choices to these discrete steps, the E6 series facilitates efficient sourcing and assembly while maintaining adequate performance for applications with broader tolerances.^[11] The values in the E6 series are derived from a geometric progression based on the sixth root of 10, where each step approximates a multiplication factor of $10^{1/6} \approx 1.467, rounded to two significant digits for practical use in engineering specifications.^[12] This logarithmic spacing ensures that the relative deviation between consecutive values remains consistent, aligning with manufacturing tolerances typically around 20% for E6-rated components. The mathematical basis of these preferred numbers originates from principles of logarithmic distribution explored in applied mathematics. Adoption of the E6 series has evolved through international standardization efforts, particularly under IEC 60063, which defines the preferred number series for electronic components to promote global uniformity.^[13] First published in 1963, the standard was revised multiple times, with the 2015 edition incorporating E3, E6, E12, E24, and finer series to accommodate advancements in precision manufacturing while retaining E6 for cost-sensitive, low-tolerance applications like basic consumer electronics and prototyping.^[14] This framework has been embraced by major component manufacturers, enabling scalable production and reducing design iteration costs in engineering projects.^[9]

Transport

Rail

The Pennsylvania Railroad's E6 class consisted of 4-4-2 "Atlantic" steam locomotives designed for high-speed passenger service, with the subclass E6s comprising 80 units built by Juniata Shops in 1914, following a single prototype E6 constructed in 1911.^[15] These locomotives featured large 80-inch (2,032 mm) driving wheels for sustained high speeds and a tractive effort of 31,275 lbf (139 kN), enabling top speeds exceeding 100 mph (160 km/h) on key routes such as the Pennsylvania Special between New York and Chicago.^[15] Their boiler, with a 76-inch diameter and superheater, provided efficient steaming, contributing to a 30% increase in power over predecessors while reducing fuel and water consumption by 23-46%.^[15] The London, Midland and Scottish Railway (LMS) Class 2P, designated under diagram E6, was a series of 0-4-4T tank engines built in 1925 at St. Rollox Works as a continuation of the Caledonian Railway's McIntosh 439 design for suburban and branch line passenger duties.^[16] Numbering 10 units (LMS equivalents to BR 55260–55269), they were equipped with inside cylinders measuring 18¼ × 26 inches and a boiler pressure of 180 psi (1.24 MPa), delivering a tractive effort of 19,200 lbf (85 kN) for short-haul operations around Glasgow and Edinburgh.^[17] These compact engines, weighing about 54 long tons (55 t), emphasized reliability on electrified or busy suburban networks like the Cathcart Circle. Both classes saw extensive use in passenger roles until the mid-20th century, with the PRR E6s phased out by dieselization in the 1950s; Pennsylvania Railroad 460 remains preserved at the Railroad Museum of Pennsylvania, notable for hauling Charles Lindbergh's 1927 transatlantic flight celebratory train.^[18] The LMS 2P engines were renumbered 55260–55269 under British Railways in 1948 and withdrawn between 1959 and 1962 amid modernization, with no examples preserved, though related Caledonian 439 class locomotive BR 55189 survives in operational condition at the Bo'ness & Kinneil Railway.

Road

The European route E6, designated under the United Nations Economic Commission for Europe (UNECE) agreement, spans approximately 3,090 km as the longest north-south E-road in the international network, serving as the primary artery along Sweden's west coast and through nearly the entire length of Norway. Established in 1975 through the European Agreement on Main International Traffic Arteries (AGR), it facilitates cross-border connectivity between the two countries, starting at Trelleborg in southern Sweden and terminating at Kirkenes in northern Norway near the Russian border. The route passes through key Swedish cities including Malmö, Helsingborg, Halmstad, Gothenburg, and Uddevalla before crossing into Norway at Svinesund, then proceeding via Oslo, Trondheim, Mo i Rana, Narvik, and other northern hubs. In Sweden, the E6 covers about 450 km as a coastal highway, functioning as the nation's main north-south corridor on the western side, linking urban centers and ports while supporting freight and tourism flows toward Norway. This segment has undergone extensive upgrades since the late 20th century, with notable expansions in the 2000s to motorway standards, including the Götaleden project in Gothenburg, which improved urban throughput with European Investment Bank funding of €65 million for road widening and safety enhancements. Bridge and tunnel projects, such as the Partihallsförbindelsen Bridge completed in the early 2010s but planned in the prior decade, addressed capacity bottlenecks; these initiatives drew on EU Trans-European Transport Network (TEN-T) support to align with broader continental infrastructure goals. Daily traffic in urban stretches near Gothenburg exceeds 30,000 vehicles, underscoring its role in regional mobility.^[19]^[20] Norway's portion, extending roughly 2,640 km, represents the longest continuous road within any single European country and integrates with national transport priorities for Arctic access and economic development. Ongoing construction history includes phased motorway conversions and resilience improvements against harsh weather, with EU co-funding aiding cross-border segments like the Svinesund border crossing upgrades in the 2000s. The route briefly intersects rail networks at major junctions, such as Oslo and Trondheim, enabling multimodal freight transfers.

Aviation

The Boeing E-6 Mercury is a strategic airborne command post and communications relay aircraft operated by the United States Navy, serving primarily in the Take Charge and Move Out (TACAMO) mission to ensure survivable nuclear command and control. Based on the Boeing 707-320 airliner airframe, it entered service in 1989 as the E-6A variant, replacing the aging EC-130Q Hercules fleet that had performed similar roles since the 1960s. The aircraft's development stemmed from a 1980s U.S. Navy program to modernize very low frequency (VLF) communications capabilities, with the first E-6A accepted in August 1989 following its maiden flight in 1987.^[21]^[22] Equipped with dual trailing-wire VLF antennas—extendable up to 5 miles in length—the E-6 Mercury enables direct communication with submerged ballistic missile submarines, forming a critical link in the nuclear triad by relaying emergency action messages from the National Command Authority even in contested environments. It supports this through a high-power VLF transmission system rated at 200 kW, allowing penetration of seawater to depths of several hundred feet. The fleet consists of 16 aircraft divided between two squadrons, Fleet Logistics Support Squadron 3 (VQ-3) and VQ-4, based at Tinker Air Force Base in Oklahoma, with a typical crew of 22 comprising officers, enlisted aircrew, and mission specialists. Operationally, the E-6 maintains continuous airborne presence, often flying racetrack patterns over the oceans to optimize antenna deployment for VLF broadcasts.^[21]^[23]^[24] The E-6B variant, introduced in 1997, expanded the platform's dual-role capabilities by integrating the airborne launch control system previously used on the Air Force's EC-135 Looking Glass aircraft, enabling it to serve as a backup command post for U.S. Strategic Command with dedicated battle staff positions for nuclear force management. The first E-6B was accepted in December 1997, and the entire fleet transitioned to this configuration by 2003, incorporating advanced satellite communications and secure data links for enhanced interoperability. Powered by four CFM International CFM56-2A-2 high-bypass turbofan engines, each producing 24,000 lbf of thrust, the aircraft achieves a maximum speed of 522 knots and a range exceeding 6,600 nautical miles with six hours of on-station loiter time, supported by aerial refueling for extended missions up to 72 hours. Its maximum takeoff weight is 342,000 pounds, allowing for substantial fuel and equipment loads to sustain long-duration operations at altitudes above 40,000 feet.^[21]^[22]^[25] As of 2025, the E-6 fleet continues to undergo modernization, including avionics upgrades by Northrop Grumman to extend service life into the 2030s, though the Navy plans its retirement post-2025 through the TACAMO Recapitalization Program, which will replace it with the E-130J Super Hercules variant to maintain unbroken operational continuity. This transition addresses the airframes' average age of nearly 35 years while preserving the essential VLF relay and command functions. The E-6 designation in aviation shares notation with unrelated U.S. military enlisted pay grades but refers exclusively here to this aircraft's NATO reporting name and mission profile.^[26]^[21]^[27]

Other transport

The Bognes–Lødingen ferry, the sole remaining maritime crossing along the European route E6 in Norway, is operated by Torghatten Nord as a double-ended roll-on/roll-off (ro-ro) vessel designed for efficient vehicle and passenger transport across the Vestfjorden in the Arctic region.^[28] The current vessel, MF Hinnøy, delivered in 2025, measures 117 meters in length with a capacity for 399 passengers and 120 passenger car units (PCU), including space for cars and trucks, and features a 4.75 MWh battery pack powering dual 1.8 MW electric motors for zero-emission operations.^[29] This ferry connects the E6's northbound and southbound segments near the Arctic Circle, providing a vital link for travelers between Bodø and Narvik while significantly reducing CO₂ emissions compared to diesel predecessors.^[30] In urban transit contexts, the E6 designation has appeared in historical European systems, though specific examples like Oslo's tram network from the mid-20th century primarily used numbered lines without a verified E6 route; modern interpretations often refer to electric bus models bearing the E6 name for sustainable city mobility. For instance, the VEFA E6 EV, a 6-meter electric minibus introduced for European fleets, features a 105.7 kWh battery enabling up to 300 km range per charge and accommodates 13+1+1 (15) passengers, supporting low-emission public transport in urban areas.^[31] Similarly, the Yutong E6, a 6.4-meter full-electric bus deployed in European trials, offers fast-charging capabilities and agile maneuverability for busy city routes, with a focus on reducing urban air pollution through its compact design and electric drivetrain.^[32] These E6-branded buses integrate into broader sustainable transport networks, often linking with major routes like the E6 highway for intermodal connectivity in northern Europe.

Other uses

Music

In music theory, the E6 chord refers to the E major sixth chord, constructed from the root note E, the major third G♯, the perfect fifth B, and the added major sixth C♯, which is the sixth degree of the E major scale.^[33] This configuration adds a subtle, colorful extension to the basic E major triad, creating a four-note harmony that evokes a sense of resolution or warmth without the tension of a seventh chord.^[34] Common voicings for the E6 chord on guitar include the open-position shape 022120, where the low E string is played open (fret 0), the A string on the second fret, the D string on the second fret, the G string on the first fret, the B string on the second fret, and the high E string open; this fingering uses the index finger on the G string first fret, middle finger on the A and B strings second fret, and ring finger on the D string second fret, allowing for a full, resonant sound when strummed from the low E.^[35] On piano, the root-position voicing places the thumb on E, index on G♯, middle on B, and ring or pinky on C♯ in the right hand, often played as a blocked chord for solid accompaniment or arpeggiated for melodic emphasis; inversions such as G♯-B-C♯-E (first inversion) facilitate smoother voice leading in progressions.^[34]^[33] The E6 chord is prevalent in jazz and pop music, where it provides added harmonic color and a retro or soulful quality, as heard in Motown tracks by artists like Aretha Franklin and in jazz standards by performers such as George Benson.^[35] In jazz theory, major sixth chords like E6 often serve as substitutes for dominant chords or appear in ii-V-I progressions, functioning as a tonic resolution (e.g., ending on E6 instead of Emaj7) to enhance melodic freedom and textural depth without altering the fundamental tonality.^[36] Their historical prominence in 20th-century harmony emerged in the late 1920s through early jazz compositions, becoming a staple by the 1930s in swing-era arrangements and pedagogical texts as a "modern" extension of triads.^[37] In standard notation, the E6 chord is represented in sheet music as "E6" or "Emaj6" above the staff, indicating the root E with the added sixth; this symbol directs performers to include the specified notes in their voicing, often in close position for piano or adapted for instrument range.^[38] Guitar tablature denotes it through fret positions, such as "e|-0--| B|-2--| G|-1--| D|-2--| A|-2--| E|-0--|" for the open voicing, aligning numeric frets with string lines to guide finger placement precisely.^[35]

Geography

The E6 postcode district lies in East London, United Kingdom, primarily within the London Borough of Newham, encompassing neighborhoods such as East Ham, Upton Park, and Beckton.^[39] This district forms part of the broader E postal area, which handles mail for much of eastern Greater London.^[40] Established in 1857 as one of the original 10 London postal districts to streamline sorting and delivery amid rapid urban expansion, the E6 system was introduced by the General Post Office to divide the city into compass-based zones for efficiency.^[40] Today, it serves 84,299 residents (2021 Census) across an area of about 4 square kilometers, featuring notable landmarks like the Grade II-listed East Ham Town Hall on Barking Road, a key civic building opened in 1905 that now houses parts of Newham Council's operations.^[39]^[41] Demographically, E6 reflects Newham's multicultural profile, with around 50% of residents identifying as Asian—predominantly South Asian communities including Indian, Pakistani, and Bangladeshi groups—alongside 27% White, 14% Black, and 4% Mixed ethnicities, based on aggregated census data.^[42] Historically, the area's population surged from under 2,000 in 1851 to over 133,000 by 1911 due to industrialization and suburban development, with further growth in the 1920s driven by interwar housing expansion that attracted working-class families from central London.^[43] This evolution from rural hamlets to dense urban suburbs continues to shape its vibrant, diverse character, supported by essential transport links including District line Underground stations at East Ham and Upton Park.^[44]

Sports

In baseball, the notation E6 designates an error charged to the shortstop, the fielder in defensive position 6, as defined in Major League Baseball's Official Rules under Rule 9.12, which specifies that an error occurs when a fielder's misplay—such as dropping a catch, fumbling a ground ball, or throwing wildly—prolongs an at-bat or allows a batter or runner to advance bases they would not have otherwise reached under ordinary effort.^[45] Common examples include a shortstop's failure to cleanly field a routine ground ball up the middle, enabling the batter to reach first base safely, or an errant throw on a double-play attempt that lets runners advance; such miscues directly affect offensive statistics, as the batter is not awarded a hit if the error is deemed responsible, and they contribute to unearned runs for pitchers. Historically, the position's high error rates are evident in early 20th-century records, where shortstops like Herman Long amassed 1,070 errors over his career from 1889 to 1904, underscoring the physical and tactical demands of turning double plays and covering vast infield territory.^[46] In chess, e6 denotes the specific square at the intersection of the e-file (the vertical column fifth from White's left, aligned with the king's bishop) and the sixth rank (the horizontal row second from Black's baseline) in the standard algebraic notation system, which FIDE mandates for all official records and uses coordinates to precisely identify each of the 64 board squares.^[47] This square gains strategic prominence in openings like the French Defense, initiated by Black's 1...e6 in response to 1.e4, a solid pawn move that supports an upcoming ...d5 advance to contest White's center while keeping the c8-h3 diagonal open for the light-squared bishop and avoiding early pawn captures.^[48] Tactics around e6 often involve pawn chain structures, such as advancing the e-pawn further or exchanging to open lines for attacks, as seen in variations like the Advance (3.e5) where White reinforces the center but concedes space. Scorekeeping and analysis tools in both sports rely on E6 and e6 notations for precision and replay value. In baseball, official scorers employ E6 in standardized scorebooks and digital platforms like the MLB Scoreboard app to log errors instantaneously, enabling post-game reviews of defensive metrics and influencing player evaluations. In chess, e6 appears in Portable Game Notation (PGN) files processed by analysis software such as ChessBase or Lichess, where engines evaluate positional motifs like pawn advances on e6 for tactical advantages in openings.

Military

The E-6 pay grade represents a mid-level enlisted rank within the United States uniformed services, governed by the Department of Defense pay scale established under the Career Compensation Act of 1949, which unified compensation structures across branches by introducing enlisted pay grades from E-1 to E-9.^[49] This system has been periodically updated through annual National Defense Authorization Acts (NDAAs), which adjust base pay rates to account for inflation, recruitment needs, and retention goals.^[50] Equivalents to the E-6 pay grade vary by branch but denote similar levels of non-commissioned officer authority: Staff Sergeant (SSG) in the Army, Technical Sergeant (TSgt) in the Air Force and Space Force, Staff Sergeant (SSgt) in the Marine Corps, and Petty Officer First Class (PO1) in the Navy and Coast Guard.^[51] As of 2025, base pay for E-6 personnel ranges from $3,276.60 per month for those with less than two years of service to $5,074.80 for those with over 18 years.^[52] Promotion to E-6 typically requires 4 to 6 years of time in service (TIS), along with minimum time in grade (TIG) thresholds that differ by branch—such as 48 months TIS and 7 months TIG for Army SSG, or equivalent professional military education and performance evaluations in other services—positioning eligible personnel for advancement to E-7.^[53]^[54] In the E-6 role, service members assume supervisory duties over junior enlisted personnel, including mentoring, conducting leadership training, and ensuring unit readiness, while preparing for higher-level command responsibilities.^[54] Following the Vietnam War, the 1970s saw significant adjustments to the E-6 pay grade as part of the transition to an all-volunteer force, including substantial pay increases enacted in 1973 and 1974 to improve recruitment and retention, alongside refinements to promotion criteria to emphasize quality over wartime expansion.^[55] These changes, authorized through NDAAs and Department of Defense policies, helped stabilize the enlisted force structure by addressing post-conflict demobilization challenges and aligning compensation with civilian wage growth.^[56]

References

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Root system of type E6. • V is the subspace of R8 consisting of points ... Number of roots: n = 72. • Base: β1 = 1. 2. (ε1 − ε2 − ε3 − ε4 − ε5 − ε6 ...
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ACCORDING TO IEC 60063. E192. E96. E48. E192. E96. E48. E192. E96. E48. E192. E96. E48. E24. E12. E6. E3. 100. 100. 100. 178. 178. 178. 316. 316. 316. 562. 562.
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Caledonian Railway 4-4-0 Express Passenger Locomotive No.721 - Dunalastair. This locomotive was built in the Company's St. Rollox Workshops in 1896 to the ...
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Nov 23, 2021 · The 8-kilometer route crosses Tysfjorden and takes about 25 minutes. This ferry is the only remaining ferry connection along European route E6, ...Missing: MF | Show results with:MF
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Powered by a robust 105,7 kWh battery, VEFA E6 EV offers a driving range of up to 300 km on a single charge. Capacity ensures reliable and eco-friendly ...
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The E6 chord is like an E major chord with an added '6th' note, and is used in pop, blues, 60s rockabilly and motown.
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For example, the II V I progression can end with a sixth chord, rather than ... Theory of Chord Progressions Root Motion In jazz, chord progressions are usually ...
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The added 6th chord will be used primarily as a Bass [i.e., in left hand accompanying chords] although it has many other uses. This is a professional MODERN ...
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(In the uncommon case that a minor added sixth is desired, it is indicated “ b6” or “ b13”.) E6. E. E‹6. E‹. E‹(b6) ! (or) add6. (or) add6. (rare). """"##. """" ...
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[41]
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Map breaking London up in sub-sections. POST 21/761. · The original 10 districts – EC (Eastern Central), WC (Western Central), and then NW, N, NE, E, SE, S, SW, ...
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East Ham is one of the 12 districts of the London Borough of Newham. The area homes a diverse community of many cultures and languages.
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These rules govern professional baseball games, including Major League and its development leagues. They are available for amateur groups, but may be modified.
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Career E Leaders:1.Herman Long/1070/, 2.Bill Dahlen/975/, 3.Germany Smith/973/, 4.Tommy Corcoran/961/, 5.Ed McKean/857/, 6.Jack Glasscock/832/, 7.Missing: 1900s | Show results with:1900s
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Algebraic notation shows you the move number, the name of the piece that is moved and then the square where the piece moves.
[48]
French Defense - Chess Openings
The French Defense starts after 1.e4 e6. Black's move by prepares the d7-d5 push to challenge White's center immediately. 1...e6 also opens lines for ...
[49]
Career Compensation Act of 1949 - Navy Cyberspace
The Career Compensation Act of 1949 was the first legislation that made reference to the primary element of Servicemembers' pay as “basic pay.”
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Basic Pay - Military Compensation
Basic pay is the main component of a Service member's compensation. The amount is determine by grade and years of service. Basic pay is a taxable income, ...Active Duty Pay · Reserve Drill Pay · FAQ
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[PDF] rank insignia of the us armed forces - Army.mil
RANK INSIGNIA OF THE U.S. ARMED FORCES. ENLISTED. E-1. E-2. E-3. E-4. E-5. E-6. E-7. E-8. E-9. SENIOR. ENLISTED. ADVISORS. ARMY no insignia. Corporal. (CPL).
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2025 Basic Pay: Enlisted - DFAS
Mar 12, 2025 · Basic Pay – Enlisted Effective April 1, 2025 ; E-6, 3,276.60, 3,606.00 ; E-5, 3,220.50, 3,466.50 ; E-4, 3,027.30, 3,182.10 ; E-3, 2,733.00, 2,904.60 ...Officers · A little about pay deductions · Wounded Warrior Pay Support
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Army Promotion to E-6 Staff Sergeant - Military-Ranks.org
Requirements for promotion to SSG are as follows: · Board appearance is 46 months TIS/five months TIG. · Earliest promotion after 48 months TIS/seven months TIG.
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Army Ranks: A Complete Guide to Enlisted and Officer Ranks
Aug 1, 2025 · Advancement to staff sergeant (E-6) often follows at six to eight years, with sergeant first class (E-7) around the eight- to 10-year mark.
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[PDF] Enlisted Personnel Management: A Historical Perspective. - DTIC
Changes in policy to aid recruitment and retention to smooth the transition to an all- volunteer force were made in 1973 and 1974, with enlistment bonuses and ...
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[PDF] ANNUAL DEFENSE DEPARTMENT REPORT FY 1975
Mar 4, 1974 · In additiont as we complete the post Vietnam adjustments in our ... On the enlisted side, there are nine different pay grades, the top five ...Missing: NDAA | Show results with:NDAA