On the solvability of a finite group by the sum of subgroup orders
| Autor: | Tărnăuceanu, Marius |
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| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Bull. Korean Math. Soc., vol. 57 (2020), no. 6, pp. 1475-1479 |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a finite group and $\sigma_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of $G$, we prove that if $\sigma_1(G)<\frac{117}{20}\,$, then $G$ is solvable. This partially solves an open problem posed in \cite{9}. |
| Databáze: | arXiv |
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