A062552
Number of cyclic subgroups of Chevalley group A_n(4) (the group of nonsingular n X n matrices over GF(4) ).
Original entry on oeis.org
2, 74, 37820, 332797040, 42906753609728, 96807463594555409408, 3287060262175777407524421632, 1849558511978449242738396356403003392, 16381469636294717667541649667987962803817283584, 2439141663752697521176587375190791943802198154311477755904
Offset: 1
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 02 2001
A060716
Singular n X n matrices over GF(4).
Original entry on oeis.org
1, 76, 80704, 1333866496, 350423140532224, 1470575268235571101696, 98701955014599602193609785344, 105983992373769699116787162453121171456, 1820806479557691387021584007269972378727328251904
Offset: 1
Avi Peretz (njk(AT)netvision.net.il), Apr 21 2001
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for n from 1 to 15 do printf(`%d,`, 4^(n^2) - product(4^n-4^j, j=0..n-1)) od:
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a(n)={4^(n^2) - prod(j=0, n - 1, 4^n - 4^j)} \\ Harry J. Smith, Jul 10 2009
A085404
Number of n X n matrices over GF(4) with rank n-1.
Original entry on oeis.org
1, 75, 79380, 1310904000, 344319762124800, 1444887697908695040000, 96976611786040182520676352000, 104131021972308383324202529613414400000, 1788970984376098024967914354100894418012733440000
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 31 2003
A220790
Product(6^n - 6^k, k=0..n-1).
Original entry on oeis.org
1, 5, 1050, 8127000, 2273284440000, 22906523331216000000, 8310241106635054164480000000, 108537128570336598656772717772800000000, 51032497739317419104816901041614046625792000000000
Offset: 0
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[1] cat [&*[(6^n - 6^k): k in [0..n-1]]: n in [1..8]]; // Bruno Berselli, Jan 28 2013
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/* By the second formula: */
m:=9;
A109354 := [6^(n*(n-1) div 2): n in [0..m-1]];
A027873 := [1] cat [&*[6^i-1: i in [1..n]]: n in [1..m]];
[A109354[i]*A027873[i]: i in [1..m]]; // Bruno Berselli, Jan 30 2013
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Table[Product[6^n - 6^k, {k, 0, n-1}], {n, 0, 60}]
A053996
Number of bases of n-dimensional vector space over GF(4).
Original entry on oeis.org
1, 3, 90, 30240, 123379200, 6462306385920, 4516376686991769600, 43295772825884473845350400, 5810971590951606258595918774272000, 11092372326294974332542866301794421571584000
Offset: 0
A335384
Order of the finite groups GL(m,q) [or GL_m(q)] in increasing order as q runs through the prime powers.
Original entry on oeis.org
6, 48, 168, 180, 480, 2016, 3528, 5760, 11232, 13200, 20160, 26208, 61200, 78336, 123120, 181440, 267168, 374400, 511056, 682080, 892800, 1014816, 1488000, 1822176, 2755200, 3337488, 4773696, 5644800, 7738848, 9999360, 11908560, 13615200, 16511040, 19845936, 24261120, 25048800, 28003968
Offset: 1
a(1) = #GL(2,2) = (2^2-1)*(2^2-2) = 3*2 = 6 and the 6 elements of GL(2,2) that is isomorphic to S_3 are the 6 following 2 X 2 invertible matrices with entries in F_2:
(1 0) (1 1) (1 0) (0 1) (0 1) (1 1)
(0 1) , (0 1) , (1 1) , (1 0) , (1 1) , (1 0).
a(2) = #GL(2,3) = (3^2-1)*(3^2-3) = 8*6 = 48.
a(3) = #GL(3,2) = (2^3-1)*(2^3-2)*(2^3-2^2) = 168.
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
- Daniel Perrin, Cours d'Algèbre, Maths Agreg, Ellipses, 1996, pages 95-115.
Cf.
A002884 [GL(m,2)],
A053290 [GL(m,3)],
A053291 [GL(m,4)],
A053292 [GL(m,5)],
A053293 [GL(m,7)],
A052496 [GL(m,8)],
A052497 [GL(m,9)],
A052498 [GL(m,11)].
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