TY  - BOOK
AU  - Bubboloni,Daniela
AU  - Spiga,Pablo
AU  - Weigel,Thomas Stefan
ED  - SpringerLink (Online service)
TI  - Normal 2-Coverings of the Finite Simple Groups and their Generalizations
T2  - Lecture Notes in Mathematics,
SN  - 9783031623486
AV  - QA174-183 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Group theory
KW  - Discrete mathematics
KW  - Graph theory
KW  - Group Theory and Generalizations
KW  - Applications of Discrete Mathematics
KW  - Graph Theory
N1  - - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-031-62348-6
ER  -