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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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[1] H. U. Besche and B. Eick, Construction of finite groups, J. Symbolic Comput., 27 (1999) 387–404. [3] K. S. Brown, Cohomology of groups, Graduate Texts in Mathematics, 87, Springer–Verlag, New York–Berlin, 1982. | ||
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