LEADER 03407nam 22005895 450 001 9910874689503321 005 20250807152924.0 010 $a9783031623486 024 7 $a10.1007/978-3-031-62348-6 035 $a(CKB)33388295200041 035 $a(MiAaPQ)EBC31552528 035 $a(Au-PeEL)EBL31552528 035 $a(DE-He213)978-3-031-62348-6 035 $a(PPN)279809999 035 $a(EXLCZ)9933388295200041 100 $a20240723d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNormal 2-Coverings of the Finite Simple Groups and their Generalizations /$fby Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (182 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2352 311 08$a9783031623479 327 $a- 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. 330 $aThis book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations. While offering readers a thorough understanding of these structures, and of the groups admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory. It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2352 606 $aGroup theory 606 $aDiscrete mathematics 606 $aGraph theory 606 $aGroup Theory and Generalizations 606 $aApplications of Discrete Mathematics 606 $aGraph Theory 615 0$aGroup theory. 615 0$aDiscrete mathematics. 615 0$aGraph theory. 615 14$aGroup Theory and Generalizations. 615 24$aApplications of Discrete Mathematics. 615 24$aGraph Theory. 676 $a512.2 700 $aBubboloni$b Daniela$01749576 701 $aSpiga$b Pablo$01367250 701 $aWeigel$b Thomas Stefan$01749577 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910874689503321 996 $aNormal 2-Coverings of the Finite Simple Groups and Their Generalizations$94183846 997 $aUNINA