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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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4502_1693ba7f5b4c90d576f9e4a98222ba48.pdf |
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| author | Bijan Taeri Ziba Tooshmalani |
| author_facet | Bijan Taeri Ziba Tooshmalani |
| author_sort | Bijan Taeri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8f0238ea44f64dc6899ca50e73f1fe61 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-8f0238ea44f64dc6899ca50e73f1fe612025-01-04T19:30:18ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-0114138739710.22103/jmmr.2024.23697.16774502Minimal non-abelian groups with an average condition on subgroupsBijan Taeri0Ziba Tooshmalani1Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, IranDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, IranFor 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.https://jmmrc.uk.ac.ir/article_4502_1693ba7f5b4c90d576f9e4a98222ba48.pdfminimal non-abelian groupsgroup element orderssum of element ordersaverage condition |
| spellingShingle | Bijan Taeri Ziba Tooshmalani Minimal non-abelian groups with an average condition on subgroups Journal of Mahani Mathematical Research minimal non-abelian groups group element orders sum of element orders average condition |
| title | Minimal non-abelian groups with an average condition on subgroups |
| title_full | Minimal non-abelian groups with an average condition on subgroups |
| title_fullStr | Minimal non-abelian groups with an average condition on subgroups |
| title_full_unstemmed | Minimal non-abelian groups with an average condition on subgroups |
| title_short | Minimal non-abelian groups with an average condition on subgroups |
| title_sort | minimal non abelian groups with an average condition on subgroups |
| topic | minimal non-abelian groups group element orders sum of element orders average condition |
| url | https://jmmrc.uk.ac.ir/article_4502_1693ba7f5b4c90d576f9e4a98222ba48.pdf |
| work_keys_str_mv | AT bijantaeri minimalnonabeliangroupswithanaverageconditiononsubgroups AT zibatooshmalani minimalnonabeliangroupswithanaverageconditiononsubgroups |