[GAP Forum] easy way to generate permutation groups?

[R. Keith Dennis]

John,

thanks!  I assumed that there must be a simple way to do this
sort of thing.


>     I don't know whether this answers the more general question which 
> you recently posed on the GAP forum but it produces two permutations u, 
> v on an appropriate interval [1..m] which generate the group which you 
> describe.
>
> gap> a := x -> [x[1],x[1]*x[2]];;
> gap> b := x -> [x[2]*x[1],x[2]];; 
> gap> g := SymmetricGroup(4);;
> gap> omega := Cartesian(g,g) ;;
> gap> u := PermListList(omega, List(omega,a));;
> gap> v := PermListList(omega, List(omega, b));;
> gap> h := Group(u,v);;
> gap> Size(h);
> 2239488
>
>     It is rather intriguing how the final group h varies with the input g.

Yes, and the size of the groups get really large quite quickly it
seems.

Thnaks again!

Keith