Year: 2024
Type: article
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.
Source: American Mathematical Monthly
Author: Nicholas J. Werner
Institution: SUNY Old Westbury
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4401516125