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vls/2603nrwcece.visuallibrary.netvdNormal 2-coverings of the finite simple groups and their generalizationsBubboloni, DanielaVerfasserautSpiga, PabloVerfasserautWeigel, ThomasVerfasserautSpringer Nature Switzerland AGVerlagpbltextTextbookszXA-CHCham, SwitzerlandSpringer[2024]© 20242024monographicengprintx, 178 Seiten 23,5 cmohne Hilfsmittel zu benutzenBandIntroduction -- 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,.Daniela Bubboloni, Pablo Spiga, Thomas Stefan WeigelGroup theoryDiscrete mathematicsGraph theoryEndliche einfache GruppeÜberdeckung9783031623479145089826499374510279906441HT030815604Online-Ausgabe9783031623486Lecture notes in mathematics2352(DE-605)HT001253222rda24080920250414144232.02561651ger https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D2561651 https://ce.visuallibrary.net/id/1333818 https://ce.visuallibrary.net/i3f/v20/1333818/manifest https://ce.visuallibrary.net/proto_ftsearch/1333818