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

Cai Heng Li; Binzhou Xia

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arXiv · 1408.0350

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

Cai Heng Li·Binzhou Xia

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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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Cai Heng Li, Binzhou Xia. 2014-08-02. Factorizations of almost simple groups with a solvable factor, and Cayley graphs of solvable groups. https://arxiv.org/abs/1408.0350

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