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＜電子ブック＞
Normal 2-Coverings of the Finite Simple Groups and their Generalizations / by Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel
(Lecture Notes in Mathematics. ISSN:16179692 ; 2352)

版	1st ed. 2024.
出版者	Cham : Springer Nature Switzerland : Imprint: Springer
出版年	2024
本文言語	英語
大きさ	X, 180 p : online resource
冊子体	Normal 2-coverings of the finite simple groups and their generalizations / Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel
著者標目	*Bubboloni, Daniela author Spiga, Pablo author Weigel, Thomas Stefan author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Discrete mathematics LCSH:Graph theory FREE:Group Theory and Generalizations FREE:Applications of Discrete Mathematics FREE:Graph Theory
一般注記	- 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, Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-031-62348-6

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