Sylow numbers and the structure of finite groups

2025/08/21 by Huaquan Wei, Yi Chen, Wei, Huaquan +5
Mathematics · Engineering · #Finite Group Theory Research #graph theory and CDMA systems #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.2508.15176

Abstract

Suppose that the finite group G=AB is a mutually permutable product of two subgroups A and B. By using Sylow numbers of A and B, we present some new bounds of the p-length l_p(G) of a p-solvable group G and the nilpotent length F_l(G) and the derived length dl(G/Φ(G)) of a solvable group G. Some known results of Zhang in J. Algebra 1995, 176 are extended.

Related

• A bound on the p-length of p-solvable groups
• An upper bound for the nonsolvable length of a finite group in terms of its shortest law
• Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p
• On the Generalized Fitting Height and Nonsoluble Length of the Mutually Permutable Products of Finite Groups
• Nonsoluble and non-p-soluble length of finite groups