[GAP Forum] Subgroups of fp groups (was:no subject)

[Alexander Konovalov]

Dear Rahul,

You need to call "Subgroup" (enter ?Subgroup in GAP to see the manual). For example,

gap> F:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> AssignGeneratorVariables(F);                       
#I  Assigned the global variables [ a, b ]
gap> G:=F/[a^4,b^2,b*a*b*a];     
<fp group on the generators [ a, b ]>
gap> g:=GeneratorsOfGroup(G);
[ a, b ]
gap> Subgroup(G,[g[1]*g[2]]);
Group([ a*b ])
gap> Size(last);
2
gap> Subgroup(G,[g[1]]);     
Group([ a ])
gap> Size(last);        
4

Note that variables a and b above are generators of the free group and not of the group G,
so I can't use Subgroup(G,[a*b]) unless I redefine them.

Hope this helps,
Alexander


On 1 Feb 2011, at 13:50, rahul kitture wrote:

> Dear Sir,
> 
> A small question regarding subgroup with generators
> When doing computations of groups on GAP, with the group given by generators
> and relations, how can we find subgroup generated by some elements of group?
> (i.e. how can we obtain subgroup generated by specific elements of group?)
> 
> 
> 
> 
> 
> -- 
> Rahul D. Kitture
> Junior Research Fellow,
> Bhaskaracharya Pratishthana
> (Research Institute for Matmematics)
> www.bprim.org
> Pune: 411 004 (India)