> < ^ Date: Thu, 04 Mar 1993 23:35:30 +0100
> < ^ From: Eamonn O'Brien <obrien@math.auckland.ac.nz >
> < ^ Subject: Re: AgGroups

Ralf Dentzer asks

But how can I see the relations of an ag group G that I read in from
e.g. the library of solvable groups or the library of 2-groups?

For groups in the 2-group or 3-group library, you access
the field G.abstractRelators described on p. 571 of the manual

gap> G := TwoGroup (32, 5);
Group( a1, a2, a3, a4, a5 )
gap> RecFields (G);
[ "generators", "identity", "isDomain", "isGroup", "isAgGroup", "cgs",
  "operations", "1", "2", "3", "4", "5", "rank", "pclass",
  "abstractGenerators", "abstractRelators" ]
gap> G.abstractRelators;
[ a1^2*a4^-1, a2^2, a2^-1*a1^-1*a2*a1*a3^-1, a3^2, a3^-1*a1^-1*a3*a1,
  a3^-1*a2^-1*a3*a2, a4^2*a5^-1, a4^-1*a1^-1*a4*a1, a4^-1*a2^-1*a4*a2,
  a4^-1*a3^-1*a4*a3, a5^2, a5^-1*a1^-1*a5*a1, a5^-1*a2^-1*a5*a2,
  a5^-1*a3^-1*a5*a3, a5^-1*a4^-1*a5*a4 ]

He also asks
>P.S. Is there a function to test for isomorphism between two
> ag groups? This would maybe solve my problem, but I

I have implemented an algorithm which in a fair number of cases
allows one to decide whether two given p-groups are isomorphic.
The ANU p-Quotient Program provides access to this implementation.
Part of that program is already accessible as a package in GAP 3.2.
See Chapter 49 of the manual.

The isomorphism testing facility is not yet accessible
within GAP -- it should be available within a few months --
however, it is part of the stand-alone program.
Any interested user should communicate *directly*
with me on this topic.

Eamonn O'Brien
School of Mathematical Sciences
Australian National University

e-mail obrien@pell.anu.edu.au

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