Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups

Characterizing factorizations of almost simple groups with a solvable factor, Li and Xia conclude that there are only several infinite families of these non-trivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. They apply the characterization to study s-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary that, except for cycles, a non-bipartite connected 3-arc transitive Cayley graph of a finite solvable group is necessarily a normal cover the Petersen graph or the Hoffman-Singleton graph. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)