Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

2015/01/22 by Martino Garonzi, Garonzi, Martino, Dan Lévy +7
Engineering · Mathematics · Medicine · #Chronic Myeloid Leukemia Treatments #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.1501.05678

openalex publication_date 2015/01/22 · arxiv created 2015/03/06 · arxiv updated 2015/03/09 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider factorizations of a finite group G into conjugate subgroups, G=A^x₁⋯ A^x_k for A≤ G and x₁,… ,x_k∈ G, where A is nilpotent or solvable. First we exploit the split BN-pair structure of finite simple groups of Lie type to give a unified self-contained proof that every such group is a product of four or three unipotent Sylow subgroups. Then we derive an upper bound on the minimal length of a solvable conjugate factorization of a general finite group. Finally, using conjugate factorizations of a general finite solvable group by any of its Carter subgroups, we obtain an upper bound on the minimal length of a nilpotent conjugate factorization of a general finite group.

Related

• Factorizing a Finite Group into Conjugates of a Subgroup
• Factorizations of finite groups
• Sylow numbers and the structure of finite groups
• Complete factorizations of finite groups
• Characterizations of the Solvable Radical