> < ^ Date: Tue, 01 Feb 1994 13:09:00 -0500
> < ^ From: Steve Fisk <fisk@polar.bowdoin.edu >
> ^ Subject: a question about fp groups

Dear Gap-forum,

If I have a group with three generators

gap> g := FreeGroup(3,"g");

and the relations

gap> g.relators := [g.1*g.2*g.3];

and I simplify the presentation

gap> h := SimplifiedFpGroup(g);

then GAP tells me that there are two generators, and no relations.

gap> h.generators;
[ g.1, g.2 ]

gap> h.relators;
[ IdWord ]

I have four questions:
1) How can I find an expression for the generator
g.3 in terms of g.1 and g.2? (In practice, there might be 20 relators;
this is just a simple example.)

2) How can I tell if an expression is the identity? e.g. g.1*g.2*g.3
(Well, this is the word problem, so can I control the time
that GAP devotes to this question - i.e. if more than 30
seconds, then return "unknown".)

3) Similarly, can I ask for Size(g) to return "unknown" if it has
to spend more than 30 seconds on it (or perhaps 10M of memory
instead of time).?

4) I asked for the size of h, and got the following. Is this a bug
or a feature?

gap> g := FreeGroup(3,"g");
Group( g.1, g.2, g.3 )

gap> g.relators := [g.1*g.2*g.3];
[ g.1*g.2*g.3 ]

gap> h := SimplifiedFpGroup(g);
Group( g.1, g.2 )

gap> Size(h);
Error, Subword: illegal <from> value at
while LengthWord( rel ^ Subword( rel, 1, 1 ) ) < LengthWord( rel ) ... in
RelatorRepresentatives( G.relators ) called from
RelsSortedByStartGen( G, table ) called from
AugmentedCosetTableMtc( G, H, 1, "_x" ) called from
D.operations.Size( D ) called from
Size( h ) called from
main loop

thanks, steve

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