Criteria for supersolvability of saturated fusion systems

2023/05/15 by Fawaz Aseeri, Aseeri, Fawaz, Julian Kaspczyk +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2305.09008

openalex publication_date 2023/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number. A saturated fusion system F on a finite p-group S is said to be supersolvable if there is a series 1 = S₀ ≤ S₁ ≤ … ≤ S_m = S of subgroups of S such that S_i is strongly F-closed for all 0 ≤ i ≤ m and such that S_i+1/S_i is cyclic for all 0 ≤ i < m. We prove some criteria that ensure that a saturated fusion system F on a finite p-group S is supersolvable provided that certain subgroups of S are abelian and weakly F-closed. Our results can be regarded as generalizations of purely group-theoretic results of Asaad.

Related

• New characterizations for supersolvability of fusion system and p-nilpotency of finite groups
• The influence of weakly SΦ-supplemented subgroups on fusion systems of finite groups
• Saturated fusion systems on p-groups of maximal class
• A generalization of Alperin fusion theorem and its applications
• Fusion systems over a Sylow p-subgroup of G₂(p)