Subgroups with a small sum of element orders
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909163127308288 |
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| author | Lazorec, Mihai-Silviu |
| author_facet | Lazorec, Mihai-Silviu |
| contents | A finite group $G$ is said to be a $\mathcal{B}_ψ$-group if $ψ(H)<|G|$ for any proper subgroup $H$ of $G$, where $ψ(H)$ denotes the sum of element orders of $H$. In this paper, we characterize the $\mathcal{B}_ψ$-groups up to the class of finite nilpotent groups. We also study the above inequality in the case of finite $P$-groups and Schmidt groups, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subgroups with a small sum of element orders Lazorec, Mihai-Silviu Group Theory A finite group $G$ is said to be a $\mathcal{B}_ψ$-group if $ψ(H)<|G|$ for any proper subgroup $H$ of $G$, where $ψ(H)$ denotes the sum of element orders of $H$. In this paper, we characterize the $\mathcal{B}_ψ$-groups up to the class of finite nilpotent groups. We also study the above inequality in the case of finite $P$-groups and Schmidt groups, respectively. |
| title | Subgroups with a small sum of element orders |
| topic | Group Theory |
| url | https://arxiv.org/abs/2404.05010 |