Orbits classifying extensions of prime power order groups
Oihana Garaialde Ocaña and Mima Stanojkovski
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Submission date: 02. Jul. 2020
MSC-Numbers: 20D15, 20E22, 20J05, 20J06
Keywords and phrases: cohomology of finite p-groups, group extensions, strong isomorphism, orbit sizes
Link to arXiv:See the arXiv entry of this preprint.
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.