A Note on Lagrange Subsets of Finite Groups
Group Theory
2025-12-30 v1
Abstract
In a finite group, a subset is called a Lagrange subset if its size divides the group order, and a factor if it admits a complementary subset. We provide a new and comparatively direct proof of the classification of groups in which every Lagrange subset is a factor. We show that any nontrivial such group must be a cyclic group of prime order, the cyclic group of order 4, or an elementary abelian group of order 4, 8, or 9.
Cite
@article{arxiv.2512.22900,
title = {A Note on Lagrange Subsets of Finite Groups},
author = {Mikhail Kabenyuk},
journal= {arXiv preprint arXiv:2512.22900},
year = {2025}
}
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8 pages