Quantitative properties on non-power subgroups of finite groups

期刊论文
发表日期：

2025年8月19日

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Jia Liu,
Wei Meng

摘要

Let G be a group and H be a subgroup of G. H is called a power subgroup of G if there exists a non-negative integer m such that $H=G^m$ $H = G^{m}$ , where $G^m:=\langle g^m:g\in G\rangle $ $G^{m} : = ⟨ g^{m} : g \in G ⟩$ . A subgroup that is not a power subgroup is a non-power subgroup. Let nps(G) denote the number of non-power subgroups of G. In this paper, we establish the lower bounds of nps(G) for finite non-cyclic nilpotent groups.