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

Binzhou Xia, Cai-Heng Li

ISBN 10: 1470453835 / ISBN 13: 9781470453831

Published by American Mathematical Society, US, 2022

About this Item

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.

Seller Inventory # LU-9781470453831

Bibliographic Details

• Title: Factorizations of Almost Simple Groups with a Solvable Factor, and Cayley Graphs of Solvable Groups
• Publisher: American Mathematical Society, US
• Publication Date: 2022
• Language: English
• ISBN 10: 1470453835
• ISBN 13: 9781470453831
• Binding: Paperback
• Condition: New
• Weight: 363 grams

About this title

Synopsis

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)