This analysis demonstrates conditions for solvability and nilpotency in finite groups, suggesting implications for subgroup classification.
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. Finally, we conclude with some open issues.
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Das et al. (2025) studied this question.
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