Dear GAP forum,

Michael Hartley's letter, copied below, has in principle already
correctly been answered by Stephan Rosebrock, namey that infiniteness
of a finitely presented group is an algorithmically undecidable
problem. However for any given finite presentation GAP provides a
variety of methods with which (in a 'trial and error' fashion) one can
try to solve the problem in this particular case. E.g. one may look
for abelian or nilpotent quotients, or for subgroups of finite index
which in turn may have infinite abelian or nilpotent quotients etc.
Since such methods can only be tried individualy 'by hand', they are
not invoked in 'IsFinite'.

I would therefore suggest that you send your presentation to
'gap-trouble' where some members of the GAP support team may have a
look if some such method may answer your particular problem. If it
does, the result should eventually been reported to the Forum, since
the question was asked there, however the rest of the Forum members
should not be bothered with the discussion that may or may not lead to
an answwer.

Kind regards Joachim Neubueser

I have a group, a quotient of a free group, and I want to check
whether or not it is infinite. I am almost certain that it is.

> What is the best way to do that? IsFinite() didn't seem like it was
going anywhere.

Yours, Mike H...

Michael Hartley : Michael.Hartley@sit.edu.my
Dean, School of Multimedia and Engineering,
Sepang Institute of Technology