Solvability of a group based on its number of subgroups

2024/03/02 by Angsuman Das, Arnab Mandal, Das, Angsuman +1 · 2 citations
Mathematics · Engineering · #05E30 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2403.01262

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.

Citations

• Classifying Groups With a Small Number of Subgroups

Cited by

• A note on finite groups with few conjugacy classes of subgroups
• The Difference Subgroup Graph of a Finite Group

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