Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups Prudence Twigg Stoked by "forever war

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Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups Prudence Twigg Stoked by "forever warA characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out 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. The characterization is then applied to study s arc transitive Cayley graphs of solvable groups, leading to a striking corollary that,