A Note on Finite Nilpotent Groups
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.
Authors
- Nicholas J. Werner (ORCID: https://orcid.org/0000-0003-1838-9678)
Institutions
- SUNY Old Westbury (US)
Publication Details
- Journal
- American Mathematical Monthly
- Published
- 2024-08-12
- DOI
- https://doi.org/10.1080/00029890.2024.2379751
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00