Orbits classifying extensions of prime power order groups

Document Type : Research Paper


1 Matematika Saila, Euskal Herriko Unibertsitatearen Zientzia eta Teknologia Fakultatea, Posta-kutxa 644, 48080 Bilbo, Spain

2 Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38123 Povo (Trento), Italy


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 the number and sizes of these orbits when the initial $p$-group is generated by at most $3$ elements.


Main Subjects

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  • Receive Date: 13 October 2020
  • Revise Date: 23 December 2022
  • Accept Date: 25 December 2022
  • Published Online: 01 March 2024