[GAP Forum] problem on finite subgroup of infinite, fp group

[Barry Monson]

Dear colleagues;
        I seek advice on the following problem.
        
        G is a finitely presented group. The presentation
has parameters I can vary, as in the order k of G.1*G.2.
I know that typically G will be infinite.
        P is a subgroup on some of the generators of G with the 
relations inherited from those of G. Typically I know P 
and it will be finite.
         Now I introduce a new relation w = 1 on G, where the word
w does not merely belong to P.
         The problem: is there some reasonable way to detect whether
the new relation lowers the the order of P? In other words, if 
N is the normal closure of <w>  in G, how can I detect whether the intersection
P \cap N is trivial?
          Notice that the G and N will usually be infinite, so that 
procedures requiring coset enumeration tend to wander into
never-never land.


Yours with thanks,
Barry Monson 
University of New Brunswick
Fredericton,   NB Canada 

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