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arXiv · 2403.01262

Solvability of a group based on its number of subgroups

Angsuman Das·Arnab Mandal
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Abstract

In this paper, we provide some conditions of (super)-solvability and nilpotency of a finite group $G$ based on its number of subgroups $Sub(G)$. Our results generalize the classification of finite groups with less than $20$ subgroups by Betz and Nash. We also provide an application of our results in studying comaximal subgroup graph of a group. Finally, we conclude with some open issues.

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Angsuman Das, Arnab Mandal. 2024-03-02. Solvability of a group based on its number of subgroups. https://doi.org/10.1080/00927872.2025.2557374

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