too many special linear matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg68687] too many special linear matrices*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Wed, 16 Aug 2006 03:36:18 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In an old group theory book they talk about special linear groups over the modulo of prime Integers: SL[2,P] The formula given is number of matrices in the group =If [n=2,6,Prime[n]*(Prime[n]^2-1)] (Essentual Student Algebra, Volume 5 ,Groups, T.S. /Blyth and E.F. Robertson,1986, Chapman and Hall,New York, page 14) So I tried to generate the elements of the group in Mathematica by a search program for Determinant one matrices. I get: 6,24,124,348 instead of what I should get: 6,12,60,168 Since the famous Klein group SL[2,7] is one of these , it would help to have a set of elements for that group! Mathematica code: Clear[M, k, s] M = {{l, m}, {n, o}}; k = 3 s = Union[Delete[Union[Flatten[Table[Flatten[Table[Table[If[Mod[Abs[Det[M]], k] - 1 == 0, M , {}], {l, 0,k - 1}], {m, 0, k - 1}], 1], {n, 0, k - 1}, {o, 0, k - 1}], 2]], 1]] Dimensions[s]

**Follow-Ups**:**Re: too many special linear matrices***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: too many special linear matrices***From:*"Carl K. Woll" <carlw@wolfram.com>