Normal 2-Coverings of the Finite Simple Groups and their Generalizations / by Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel.

Format:

Book

Author/Creator:

Bubboloni, Daniela.

Contributor:

Spiga, Pablo.

Weigel, Thomas Stefan.

Series:

Lecture Notes in Mathematics, 1617-9692 ; 2352

Language:

English

Subjects (All):

Group theory.

Discrete mathematics.

Graph theory.

Group Theory and Generalizations.

Applications of Discrete Mathematics.

Graph Theory.

Local Subjects:

Group Theory and Generalizations.

Applications of Discrete Mathematics.

Graph Theory.

Physical Description:

1 online resource (182 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

This book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,.

Contents:

- Introduction

Preliminaries

Linear groups

Unitary groups

Symplectic groups

Odd dimensional orthogonal groups

Orthogonal groups with Witt defect 1

Orthogonal groups with Witt defect 0

Proofs of the main theorems

Almost simple groups having socle a sporadic simple group

Dropping the maximality

Degenerate normal 2-coverings.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9783031623486

OCLC:

1450101995