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
مقاله 7، دوره 13، شماره 1، خرداد 2024، صفحه 63-95 اصل مقاله (573.25 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