New characterizations for supersolvability of fusion system and p-nilpotency of finite groups

2023/12/25 by Shengmin Zhang, Zhang, Shengmin, Zhencai Shen +1
Computer Science · Mathematics · #20D10 #20D15 #20D20 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2402.01073

openalex publication_date 2023/12/25 · openalex created_date 2024/02/06 · openalex updated_date 2026/07/28

Abstract

Let p be a prime, S be a p-group and F be a saturated fusion system over S. Then F is said to be supersolvable, if there exists a series of S, namely 1 = S₀ ≤ S₁ ≤ ⋯ ≤ S_n = S, such that S_i+1/S_i is cyclic, i=0,1,⋯, n-1, S_i is strongly F-closed, i=0,1,⋯,n. In this paper, we investigate the characterizations for supersolvability of F_S (G) under the assumption that certain subgroups of G satisfy different kinds of generalized normalities in section \ref1003. Moreover, we obtain the more advanced and remarkable result of characterizations for generalized saturated fusion system F in section \refSection 4. Finally, we apply the results in section \ref1003 and \refSection 4 and give characterizations for p-nilpotency of finite groups under the assumption that some subgroups of G satisfy different kinds of generalized normalities.

Related

• Criteria for supersolvability of saturated fusion systems
• The influence of weakly SΦ-supplemented subgroups on fusion systems of finite groups
• Criteria for nilpotency of fusion systems
• Saturated fusion systems on p-groups of maximal class
• A further generalization of the Glauberman-Thompson p-nilpotency criterion in fusion systems