Factorizations of almost simple groups with a solvable factor, and cayley graphs of solvable groups / Cai Heng Li, Binzhou Xia.

Format:

Book

Author/Creator:

Li, Cai Heng, author.

Xia, Binzhou, author.

Series:

Memoirs of the American Mathematical Society ; no.1375.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1375

Language:

English

Subjects (All):

Finite groups.

Group theory.

Algebra.

Graph theory.

Graphic methods.

Solvable groups.

Physical Description:

v, 99 pages ; 26 cm

Place of Publication:

Providence : American Mathematical Society, 2022.

Summary:

"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 nontrivial 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 Hoffman-Singleton graph"-- Provided by publisher.

Contents:

Introduction

Preliminaries

The factorization of linear and unitary groups of prime dimension

Non-classical groups

Examples in classical groups

Reduction for classical groups

Proof of Theorem 1.1

s-Arc-transitive Cayley graphs of solvable groups

Appendix A. Tables for nontrivial maximal factorizations of almost simple classical groups.

Notes:

Includes bibliographical references.

Other Format:

Online version:

ISBN:

9781470453831

1470453835

OCLC:

1343646135