Factorizing a Finite Group into Conjugates of a Subgroup

2014/07/22 by Dan Lévy, Martino Garonzi, Levy, Dan +1 · 1 citation
Engineering · Mathematics · Medicine · #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1407.5937

openalex publication_date 2014/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every non-nilpotent finite group G, there exists at least one proper subgroup M such that G is the setwise product of a finite number of conjugates of M. We define γ_cp( G) to be the smallest number k such that G is a product, in some order, of k pairwise conjugated proper subgroups of G. We prove that if G is non-solvable then γ_cp( G) ≤36 while if G is solvable then γ_cp( G) can attain any integer value bigger than 2, while, on the other hand, γ_cp( G) ≤4log₂\vert G\vert .

Citations

• Unitriangular factorisations of Chevalley groups

Cited by

• The Difference Subgroup Graph of a Finite Group

Related

• Factorizations of finite groups by conjugate subgroups which are\n solvable or nilpotent
• Groups equal to a product of three conjugate subgroups
• Some problems about products of conjugacy classes in finite groups
• A note on finite groups with few conjugacy classes of subgroups
• Characterizations of the Solvable Radical