Re: finite group theory w/mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg71275] Re: [mg71227] finite group theory w/mathematica*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 12 Nov 2006 06:48:59 -0500 (EST)*References*: <200611110837.DAA27417@smc.vnet.net>

On 11 Nov 2006, at 17:37, Christopher Arthur wrote: > Has anyone had luck using mathematica for finite group theory? > > We were playing with the Combinatorica package, but we couldn't figure > out, for example, how to show the subgroup structure of a permutation > group. chris arthur > Load the Combinatorica package: << DiscreteMath`Combinatorica` define group multiplication: mult[x_?PermutationQ, y_?PermutationQ] := Permute[x, y] now the multiplication table for the symmetric group on 5 elements is given by: MultiplicationTable[SymmetricGroup[5], mult] The entries in the table are integers form 1 to 5!, so that the integer n stands for the n-th element in SymmetricGroup[5][n]. For example: SymmetricGroup[5][[109]] {5,3,1,2,4} If yu prefer, you can make a multiplication table with the actual group elements (permutations)a s entries: MultiplicationTable[SymmetricGroup[5],mult] /. n_Integer :> SymmetricGroup[5][[n]] Make sure you use TraditionalForm for the output or else wrap TableForm around the last line. Andrzej Kozlowski

**References**:**finite group theory w/mathematica***From:*Christopher Arthur <caa0012@unt.edu>