Factorizations of almost simple groups with a solvable factor, and Cayley graphs of solvable groups
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Bibliographic Information
Factorizations of almost simple groups with a solvable factor, and Cayley graphs of solvable groups
（Memoirs of the American Mathematical Society, no. 1375）
American Mathematical Society, c2022
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"September 2022, volume 279, number 1375 (fourth of 6 numbers)"
Includes bibliographical references (p. 97-99)
Description and Table of Contents
Description
A 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, except for cycles, a non-bipartite connected 3-arc-transitive Cayley graph of a finite solvable group is necessarily a normal cover of the Petersen graph or the Ho?man-Singleton graph.
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