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Minimal non-abelian groups with an average condition on subgroups | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 387-397 اصل مقاله (484.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23697.1677 | ||
| نویسندگان | ||
| Bijan Taeri* ؛ Ziba Tooshmalani | ||
| Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran | ||
| چکیده | ||
| For a finite group $G$, the average order $o(G)$ is defined to be the average of all order elements in $G$. We say that $G$ satisfies the average condition if $o(H)\leq o(G)$ for all subgroups $H$ of $G$. In [On a question of Jaikin-Zapirain about the average order elements of finite groups, Int. J. Group Theory, To appear] we proved that every abelian group satisfies the average condition. In this paper, we classify minimal non-abelian groups which satisfy the average condition. | ||
| کلیدواژه‌ها | ||
| Minimal non-abelian groups؛ Group element orders؛ Sum of element orders؛ Average condition | ||
| مراجع | ||
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[15] Tarnauceanu M. (To appear). A caracterization of A5 by its average order, Int. J. Group Theory, http://dx.doi.org/10.22108//IJGT.2023.138637.1866
[16] Taeri B., & Tooshmalani Z. (To appear). On a question of Jaikin-Zapirain about the average order elements of nite groups, Int. J. Group Theory, http://dx.doi.org/10.22108/IJGT.2024.139508.1879 | ||
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