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MiS Preprint
74/2020

Orbits classifying extensions of prime power order groups

Oihana Garaialde Ocaña and Mima Stanojkovski

Abstract

The strong isomorphism classes of extensions of finite groups are parametrized by orbits of a prescribed action on the second cohomology group. We study these orbits in the case of extensions of a finite abelian $p$-group by a cyclic factor of order $p$. As an application, we compute number and sizes of these orbits when the initial $p$-group is generated by at most $3$ elements.

Received:
02.07.2020
Published:
02.07.2020
MSC Codes:
20D15, 20E22, 20J05, 20J06
Keywords:
cohomology of finite p-groups, group extensions, strong isomorphism, orbit sizes

Related publications

inJournal
2024 Journal Open Access
Oihana Garaialde Ocaña and Mima Stanojkovski

Orbits classifying extensions of prime power order groups

In: International journal of group theory, 13 (2024) 1