July 7, 2024Open Access

A Note on Finite Nilpotent Groups

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Abstract

It is well known that if G is a group and H is a normal subgroup of G of finite index k, then xᵏ H for every x G. We examine finite groups G with the property that xᵏ 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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Nicholas J. Werner (Sun,) studied this question.

synapsesocial.com/papers/68e6128fb6db6435875a52e9 https://doi.org/https://doi.org/10.48550/arxiv.2407.05498

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