Factorizations of almost simple groups with a solvable factor, and   Cayley graphs of solvable groups
  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. 
Cai Heng Li, Binzhou Xia
math.GR