Agemo not working for trivial groups

[laurentbartholdi]

In the latest gap, I encounter the following problem:

gap> List(AllSmallGroups(2^7),x->Agemo(Agemo(x,2,1),2,1));
Error, Agemo: <G> must be a p-group at /usr/local/src/gap/lib/grp.gi:2283 called from
Agemo( Agemo( x, 2, 1 ), 2, 1 ) at *errin*:1 called from
func( C[i] ) at /usr/local/src/gap/lib/coll.gi:663 called from
Error( "Agemo: <G> must be a p-group" ); at /usr/local/src/gap/lib/grp.gi:2283 called from
Agemo( Agemo( x, 2, 2 ), 2, 1 ) at *stdin*:1 called from
func( elm ) at /usr/local/src/gap/lib/coll.gi:1456 called from

The problem seems to be that if Agemo, say, creates a trivial subgroup of a p-group, then it is marked as being a p-group, but its prime p is forgotten. Then the prime p is recomputed by PrimePGroup, which looks at orders of generators rather than remembering.

The problem can be "fixed" by InstallOtherMethod(PrimePGroup,[IsGroup],1000,x->2);

[fingolfin]

There is no mathematical valid return value for PrimePGroup for the trivial group. If you read the documentation for PrimePGroup it explicitly states that it returns fail for trivial groups.

However Agemo should handle trivial groups as input. I'll open a PR fixing that.

[laurentbartholdi]

Mathematically, I definitely agree with you... but I was under the impression that there was a subcategory p-group of pc-group, which stored the prime. I believe that would make sense, and then I could argue that PrimePGroup should return the prime of the category. In other words, there could be a different trivial group of order p^0 for all primes p.

…

On Fri, 25 Aug 2023 at 10:02, Max Horn ***@***.***> wrote: There is no mathematical valid return value for PrimePGroup for the trivial group. If you read the documentation for PrimePGroup it explicitly states that it returns fail for trivial groups. However Agemo should handle trivial groups as input. I'll open a PR fixing that. — Reply to this email directly, view it on GitHub <#5492 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AARAQUFYVFUT4LOZZMUMFHLXXBLX5ANCNFSM6AAAAAA3XG2UYU> . You are receiving this because you authored the thread.Message ID: ***@***.***>

-- Laurent Bartholdi laurent.bartholdi<at>gmail<dot>com Fachrichtung Informatik+Mathematik, Universität des Saarlandes Postfach 151150, 66041 Saarbrücken, Germany Tel. +49 681 3023227, Sekr. +49 681 3023430

[fingolfin]

Your impression was wrong then, the documentation is quite explicit about this, too.