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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