On the solvability of a finite group by the sum of subgroup orders
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916402486575104 |
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| author | Tărnăuceanu, Marius |
| author_facet | Tărnăuceanu, Marius |
| contents | Let $G$ be a finite group and $σ_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of $G$, we prove that if $σ_1(G)<\frac{117}{20}\,$, then $G$ is solvable. This partially solves an open problem posed in \cite{9}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the solvability of a finite group by the sum of subgroup orders Tărnăuceanu, Marius Group Theory Let $G$ be a finite group and $σ_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of $G$, we prove that if $σ_1(G)<\frac{117}{20}\,$, then $G$ is solvable. This partially solves an open problem posed in \cite{9}. |
| title | On the solvability of a finite group by the sum of subgroup orders |
| topic | Group Theory |
| url | https://arxiv.org/abs/2409.13077 |