Orbits classifying extensions of prime power order groups
نویسندگان
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
doi
10.22108/ijgt.2022.125417.1651چکیده
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.
