A bound on the p-length of p-solvable groups

2013/11/26 by Jon González‐Sánchez, Jon Gonzalez-Sanchez, Gonzalez-Sanchez, Jon +2
Mathematics · #20D10 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR #msc:20D10

paper · pdf · doi:10.48550/arxiv.1311.6665

5 pages

arxiv created 2013/11/26 · openalex publication_date 2013/11/26 · arxiv updated 2013/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite p-solvable group and P a Sylow p-subgroup of G. Suppose that γ_l(p-1)(P)⊆ γ_r(P)^ps for l(p-1)<r+s(p-1), then the p-length is bounded by a function depending on l.

Related

• Sylow numbers and the structure of finite groups
• The powerful class of Sylow subgroups of finite groups
• Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p
• An affirmative answer to a conjecture related to the solvability of groups
• A cohomological criterion for p-solvability