Factorizations of almost simple groups with a solvable factor, and Cayley graphs of solvable groups

2014/08/02 by Cai Heng Li, Li, Cai Heng, Binzhou Xia +1
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.1408.0350

openalex publication_date 2014/08/02 · arxiv created 2016/02/25 · arxiv updated 2016/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classification is given for factorizations of almost simple groups with at least one factor solvable, and it is then applied to characterize s-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary: Except the cycles, every non-bipartite connected 3-arc-transitive Cayley graph of a solvable group is a cover of the Petersen graph or the Hoffman-Singleton graph.

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