Re: too many special linear matrices->error in number

*To*: mathgroup at smc.vnet.net*Subject*: [mg68716] Re: too many special linear matrices->error in number*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Thu, 17 Aug 2006 04:18:23 -0400 (EDT)*References*: <ebuju2$6lf$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

SL[2,P]-> number of matrices in the group =If [n=2,6,Prime[n]*(Prime[n]^2-1)] PSL[2,P]-> number of matrices in the group =If [n=2,6,Prime[n]*(Prime[n]^2-1)/2] Half as many for PSL except for p=2... Still the program is wrong for primes 5 and 7! Roger Bagula wrote: >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] > > >