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arXiv · 2409.13077

On the solvability of a finite group by the sum of subgroup orders

Marius Tărnăuceanu
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Abstract

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}.

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Marius Tărnăuceanu. 2024-09-19. On the solvability of a finite group by the sum of subgroup orders. https://arxiv.org/abs/2409.13077

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