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Re: finite group theory w/mathematica


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


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