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arXiv · 2512.22900

A Note on Lagrange Subsets of Finite Groups

Mikhail Kabenyuk
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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.

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Mikhail Kabenyuk. 2025-12-28. A Note on Lagrange Subsets of Finite Groups. https://arxiv.org/abs/2512.22900

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