> < ^ Date: Sun, 13 Oct 2002 14:37:38 +0200 (MEST)
> < ^ From: Marco Costantini <costanti@giove.mat.uniroma1.it >
> < ^ Subject: Re: IsomorphismGroups

Dear gap forum and dear Alexander Konovalov,
let G, H be your groups and n a positive integer.

A possibility to decide isomorphism of p-groups in Gap is provided by Anu
Pq package (if you have an unix machine and this package installed).

RequirePackage("anupq");
IsPqIsomorphicPGroup (G, H);

A possibility to prove isomorphism of Pc groups is provided by the
function RandomIsomorphismTest :

list := [G, H];
code := List( list, CodePcGroup );
code := List( code, x -> rec( code := x, order := 2^10 ) );
RandomIsomorphismTest( code, n );

John McKay wrote:
> Compute Auto group and nilpotency class. These may be different.
A possibility to prove non-isomorphism of groups is by going
further in this direction and computing and comparing the sizes of the
"natural" subgroups of G and H.
Try some commands like this:

List(PCentralSeries(G), Size) = List(PCentralSeries(H), Size);

I leave to you to find which possibility is useful for your needs.

Best wishes,
Marco Costantini

Dear Forum,

I have a pair of 2-groups of size 1024 which are likely to be
non-isomorhic. On current stage I am interested in obtaining an answer
yes or not, and not in finding an isomorhism if the answer is "yes".
This groups are PcGroups, so they have 10 generators, which is not the
MinimalGeneratingSet. Is it better to generate a pair of another groups
with Group(MinimalGeneratingSet(G)) and then apply IsomorphismGroups to
this new pair ? Are there any another approaches ?

Sincerely yours,
Alexander Konovalov

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