A Note on Lagrange Subsets of Finite Groups

2025/12/28 by Kabenyuk, Mikhail
#20D60 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2512.22900

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.

Citations

• Groups in which every Lagrange subset is a factor
• Factorizations of simple groups of order 168 and 360
• Complete factorizations of finite groups
• Factorizations in finite groups

Related

• Groups in which every Lagrange subset is a factor
• Finite groups with specific number of cyclic subgroups
• A connection between the number of subgroups and the order of a finite group
• Group Structures on Families of Subsets of a Group
• Groupes satisfaisant une condition nilpotence