Orbits classifying extensions of prime power order groups

Garayalde, Oihana; Stanojkovski, Mima

doi:10.22108/ijgt.2022.125417.1651

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	Orbits classifying extensions of prime power order groups
International Journal of Group Theory
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 04 دی 1401 اصل مقاله (588.38 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2022.125417.1651
نویسندگان
Oihana Garayalde^* ¹؛ Mima Stanojkovski²
¹Matematika Saila, Euskal Herriko Unibertsitatearen Zientzia eta Teknologia Fakultatea, Posta-kutxa 644, 48080 Bilbo, Spain
²Dipartimento di Matematica, Università di Trento, via Sommarive 14, 38123 Povo (Trento), Italy
چکیده
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.
کلیدواژه‌ها
Cohomology of finite $p$-groups؛ group extensions؛ strong isomorphism؛ orbit sizes

مراجع
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Orbits classifying extensions of prime power order groups