Factorizations of simple groups of order 168 and 360

2024/01/17 by M. I. Kabenyuk, Kabenyuk, Mikhail · 1 citation
Engineering · Mathematics · Neuroscience · #20B30 #20D40 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Nuclear Receptors and Signaling #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2401.09306

openalex publication_date 2024/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A finite group G is called k-factorizable if for any factorization |G|=a₁⋯ a_k with a_i>1 there exist subsets A_i of G with |A_i|=a_i such that G=A₁⋯ A_k. We say that G is multifold-factorizable if G is k-factorizable for any possible integer k≥2. We prove that simple groups of orders 168 and 360 are multifold-factorizable and formulate two conjectures that the symmetric group S_n for any n and the alternative group A_n for n≥6 are multifold-factorizable.

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