[GAP Forum] Finding [2,p]-generated groups

[R. Keith Dennis]

Dear Alexander,

thanks for the suggestion.  I guess "simplest way to go" for me
meant that I knew the additional reduction one could make, but
it wasn't clear to me how much it would help to speed up the
computation.  Or it might simply reflect on the level of my
programming skills ...  

But in any case I would not thought of using GQuotients for this
purpose, as I was not thinking of answering a more specific question,
where the second element was restricted.

Thanks again for the comments & examples!

Keith

> > testing all relevant ones seems like the simplest way to go.

> It is possible to select the second element up to conjugacy with the  
> centralizer of the first element. (A nice description is in section  
> 9.1 of Holt, Eick, O'Brien: Handbook of CGT).
>
> The easiest way to do this in GAP is to use the function GQuotients  
> on a suitable finitely presented group:
> For example one case for p=11:
>
> gap> f:=FreeGroup("x","y");
> <free group on the generators [ x, y ]>
> gap> AssignGeneratorVariables(f);
> #I  Assigned the global variables [ x, y ]
> gap> rels:=[x^2,y^11]; #e.g. p=11
> [ x^2, y^11 ]
> gap> g:=f/rels;
> <fp group on the generators [ x, y ]>
> gap> h:=MathieuGroup(11);
> Group([ (1,2,3,4,5,6,7,8,9,10,11), (3,7,11,8)(4,10,5,6) ])
> gap> GQuotients(g,h);
> [ [ x, y ] -> [ (4,10)(5,8)(6,7)(9,11), (1,6,2,10,3,4,8,7,11,9,5) ],
>    ...
>
> This lists one representative per conjugacy class of generating  
> systems. The list returned is empty iff no generating system exists.
>
> I hope this is of help,
>
>       Alexander
>
>