Minimal non-abelian groups with an average condition on subgroups
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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4502_1693ba7f5b4c90d576f9e4a98222ba48.pdf |
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| Summary: | 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. |
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| ISSN: | 2251-7952 2645-4505 |