A052496
Number of nonsingular n X n matrices over GF(8).
Original entry on oeis.org
1, 7, 3528, 115379712, 241909719367680, 32467582052437076213760, 278893342293098904613804037898240, 153323163270070838469523866093442017326530560
Offset: 0
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[1] cat [&*[(8^n-8^k): k in [0..n-1]]: n in [1..10]]; // Bruno Berselli, Jan 30 2013
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Table[Product[(8^n - 8^j), {j, 0, n-1}], {n, 0, 10}] (* G. C. Greubel, May 14 2019 *)
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{a(n) = prod(j=0,n-1, 8^n - 8^j)}; \\ G. C. Greubel, May 14 2019
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[product(8^n - 8^j for j in (0..n-1)) for n in (0..10)] # G. C. Greubel, May 14 2019
A052497
Number of nonsingular n X n matrices over GF(9).
Original entry on oeis.org
1, 8, 5760, 339655680, 1624314979123200, 629282246371356907929600, 19747506525777609095698646040576000, 50195501537943419769100848121708339934527488000
Offset: 0
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[1] cat [&*[(9^n - 9^k): k in [0..n-1]]: n in [1..10]]; // Bruno Berselli, Jan 28 2013
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Table[Product[(9^n - 9^j), {j, 0, n-1}], {n, 0, 10}] (* G. C. Greubel, May 14 2019 *)
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{a(n) = prod(j=0,n-1, 9^n - 9^j)}; \\ G. C. Greubel, May 14 2019
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[product(9^n - 9^j for j in (0..n-1)) for n in (0..10)] # G. C. Greubel, May 14 2019
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}]
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)].
Showing 1-4 of 4 results.
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