A Note on Finite Nilpotent Groups

2024/07/07 by Werner, Nicholas J.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2407.05498

Abstract

It is well known that if G is a group and H is a normal subgroup of G of finite index k, then x^k ∈ H for every x ∈ G. We examine finite groups G with the property that x^k ∈ H for every subgroup H of G, where k is the index of H in G. We prove that a finite group G satisfies this property if and only if G is nilpotent.

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