Normal 2-Coverings of the Finite Simple Groups and their Generalizations
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....
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| Автори: | , , |
|---|---|
| Співавтор: | |
| Формат: | Електронний ресурс eКнига |
| Мова: | Англійська |
| Опубліковано: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
|
| Редагування: | 1st ed. 2024. |
| Серія: | Lecture Notes in Mathematics,
2352 |
| Предмети: | |
| Онлайн доступ: | https://doi.org/10.1007/978-3-031-62348-6 |
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| 100 | 1 | |a Bubboloni, Daniela. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Normal 2-Coverings of the Finite Simple Groups and their Generalizations |h [electronic resource] / |c by Daniela Bubboloni, Pablo Spiga, Thomas Stefan Weigel. |
| 250 | |a 1st ed. 2024. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2024. | |
| 300 | |a 1 online resource (X, 180 p.). | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2352 | |
| 505 | 0 | |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. | |
| 520 | |a 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,. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Discrete mathematics. | |
| 650 | 0 | |a Graph theory. | |
| 650 | 1 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Applications of Discrete Mathematics. |
| 650 | 2 | 4 | |a Graph Theory. |
| 700 | 1 | |a Spiga, Pablo. |e author. |0 (orcid)0000-0002-0157-7405 |1 https://orcid.org/0000-0002-0157-7405 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Weigel, Thomas Stefan. |e author. |0 (orcid)0000-0003-1183-779X |1 https://orcid.org/0000-0003-1183-779X |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2352 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-62348-6 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||