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On numbers which are orders of nilpotent groups with bounded class | ||
| International Journal of Group Theory | ||
| مقاله 5، دوره 14، شماره 2، شهریور 2025، صفحه 93-97 اصل مقاله (365.95 K) | ||
| نوع مقاله: Ischia Group Theory 2022 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2023.137950.1851 | ||
| نویسنده | ||
| Maria Ferrara* | ||
| Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”, viale Lincoln 5, Caserta (Italy) | ||
| چکیده | ||
| Let $n$ be a positive integer. In this short note, we characterize those numbers $m$ for which any group of order $m$ is an $n$-Engel group and those numbers $m$ for which any group of order $m$ has all its subgroups subnormal of defect at most $n$. | ||
| کلیدواژهها | ||
| Engel group؛ subnormal subgroup؛ defect | ||
| مراجع | ||
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[1] Y. Berkovich, Groups of prime power order, 1, With a foreword by Zvonimir Janko, De Gruyter Expositions in Mathematics, 46, Walter de Gruyter GmbH & Co. KG, Berlin, 2008. [6] T. W. Müller, An arithmetic theorem related to groups of bounded nilpotency class, J. Algebra, 300 no. 1 (2006) 10–15. | ||
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