Complete factorizations of finite groups

2023/11/13 by M. I. Kabenyuk, Kabenyuk, Mikhail · 1 citation
Engineering · Mathematics · #20D60 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2311.07061

openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group. The subsets A₁,…,A_k of G form a complete factorization of group G if if they are pairwise disjoint and each element g∈ G is uniquely represented as g=a₁… a_k, with a_i∈ A_i. We prove the following theorem: Let G be a finite nilpotent group. If |G|=m₁… m_k where m₁,…,m_k are integers greater 1 and k≥3, then there exist subsets A₁,…,A_k of G which form a complete factorization of group G and |A_i|=m_i for all i=1,2,…,k. In addition, we give several examples of building complete factorization for some groups and formulate one open question.

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• A Note on Lagrange Subsets of Finite Groups

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