03671nam a22005655i 4500 978-3-031-62348-6 DE-He213 20251030112643.0 cr nn 008mamaa 240723s2024 sz | s |||| 0|eng d 9783031623486 978-3-031-62348-6 10.1007/978-3-031-62348-6 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema Bubboloni, Daniela. author. aut http://id.loc.gov/vocabulary/relators/aut 81056 Normal 2-Coverings of the Finite Simple Groups and their Generalizations [electronic resource] / by Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. X, 180 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 2352 - 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. 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,. Group theory. 70149 Discrete mathematics. Graph theory. Group Theory and Generalizations. 70154 Applications of Discrete Mathematics. 67427 Graph Theory. Spiga, Pablo. author. aut http://id.loc.gov/vocabulary/relators/aut 81057 Weigel, Thomas Stefan. author. aut http://id.loc.gov/vocabulary/relators/aut 81058 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031623479 Printed edition: 9783031623493 Lecture Notes in Mathematics, 1617-9692 ; 2352 75434 https://doi.org/10.1007/978-3-031-62348-6 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 61818 61818