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A059238 Orders of the finite groups GL_2(K) when K is a finite field with q = p^m elements for a prime p and m >= 1. 3
6, 48, 180, 480, 2016, 3528, 5760, 13200, 26208, 61200, 78336, 123120, 267168, 374400, 511056, 682080, 892800, 1014816, 1822176, 2755200, 3337488, 4773696, 5644800, 7738848, 11908560, 13615200, 16511040, 19845936, 25048800, 28003968 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..29.

R. A. Wilson, The classical groups, chapter 3.3.1 in The finite Simple Groups, Graduate Texts in Mathematics 251 (2009).

FORMULA

If the finite field K has p^m elements the order of the group GL_2(K) is (p^(2m)-1)*(p^(2m) - p^m) = (p^m+1)*(p^m)*(p^m-1)^2

EXAMPLE

a(4) = 480 because (5^2-1)*(5^2-5) = 480.

MAPLE

with(numtheory): for n from 2 to 400 do if nops(ifactors(n)[2]) = 1 then printf(`%d, `, (n+1)*(n)*(n-1)^2) fi: od:

MATHEMATICA

nn=30; a=Take[Union[Sort[Flatten[Table[Table[Prime[m]^k, {m, 1, nn}], {k, 1, nn}]]]], nn]; Table[(q^2-1)(q^2-q), {q, a}]  (* Geoffrey Critzer, Apr 20 2013 *)

CROSSREFS

Subset of A047927.

Cf. A000961

Sequence in context: A244726 A005353 A047927 * A254832 A026695 A208536

Adjacent sequences:  A059235 A059236 A059237 * A059239 A059240 A059241

KEYWORD

nonn

AUTHOR

Avi Peretz (njk(AT)netvision.net.il), Jan 21 2001

EXTENSIONS

More terms from James A. Sellers, Jan 22 2001

STATUS

approved

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Last modified July 16 04:09 EDT 2019. Contains 325064 sequences. (Running on oeis4.)