[GAP Forum] Re: Free group from generators

[Alexander Hulpke]

Dear GAP Forum,


Randy Cone asked:

 >  Is there a way to find the number of generators of a free group,  
based on a
 > word from that free group?  I.E., is there some way to "talk  
about" the group
 > of origin of an (associative) word in GAP?



Yes. You can get the group from the family:

gap> f:=FreeGroup(2);
<free group on the generators [ f1, f2 ]>
gap> a:=f.1;
f1
gap> FamilyObj(a)!.freeGroup;
<free group on the generators [ f1, f2 ]>

 > Better, can I determine the number of generators based solely on  
the GAP
 > object "g" below?:


You can ask for the Length of the GeneratorsOfGroup of the free group  
you
got this way.

Best,

    Alexander Hulpke