Normal 2-Coverings of the Finite Simple Groups and Their Generalizations

• Autore: Bubboloni Daniela
• Pubblicazione: Cham : , : Springer, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (182 pages)
• Altri autori: SpigaPablo WeigelThomas Stefan
• Nota di contenuto: Intro -- Preface -- Acknowledgement -- Contents -- 1 Introduction -- 1.1 The Weak Normal Covering Number and the Normal Covering Number of the Finite Non-abelian Simple Groups -- 1.2 The Normal 2-Coverings of the Almost Simple Groups and the Weak Normal Covering Number of the Almost Simple Groups -- 1.3 The Invariably Generating Graph and the Aut-invariably Generating Graph -- 1.4 The Erdős-Ko-Rado Theorem and the Derangement Graph -- 1.5 Further on Derangements: The Boston-Shalev Conjecture -- 1.6 Normal 2-Coverings for Arbitrary Finite Groups -- 1.7 Normal Coverings and Kronecker Classes -- 1.8 Structure of the Book and Comments -- 2 Preliminaries -- 2.1 Classical Groups -- 2.2 Normal and Weak Normal Coverings of Classical and Simple Classical Groups -- 2.3 From Weak Normal Coverings to Normal Coverings -- 2.4 Action of on Its Natural Module -- 2.5 Huppert's Theorem and Singer Cycles -- 2.6 Some Arithmetics -- 2.7 Primitive Prime Divisors -- 2.8 Further Facts on Singer Cycles -- 2.9 The ppd-Elements -- 2.10 Bertrand Elements -- 2.11 The Spinor Norm and the Bertrand Elements -- 3 Linear Groups -- 4 Unitary Groups -- 4.1 Small Dimensional Unitary Groups -- 4.2 Large Dimensional Unitary Groups -- 5 Symplectic Groups -- 5.1 Small Dimensional Symplectic Groups -- 5.2 Large Dimensional Symplectic Groups -- 6 Odd Dimensional Orthogonal Groups -- 6.1 Small Odd Dimensional Orthogonal Groups -- 6.2 Large Odd Dimensional Orthogonal Groups -- 6.3 An Auxiliary Result -- 7 Orthogonal Groups with Witt Defect 1 -- 7.1 Small Even Dimensional Orthogonal Groups of Witt Defect 1 -- 7.2 Large Even Dimensional Orthogonal Groups of Witt Defect 1 -- 8 Orthogonal Groups with Witt Defect 0 -- 8.1 Orthogonal Groups of Witt Defect 0 of Dimension at Least 10 -- 8.2 Eight Dimensional Orthogonal Groups with Witt Defect 0 -- 9 Proofs of the Main Theorems. ; 10 Almost Simple Groups Having Socle a Sporadic Simple Group -- 11 Dropping the Maximality -- 11.1 Linear Groups: Cases (3)-(7) -- 11.2 Unitary Groups: Cases (8) and (9) -- 11.3 Exceptional Groups: Case (2) -- 11.4 Exceptional Groups: Case (1) -- 11.5 Symplectic Groups: Cases (10) and (11) -- 11.6 Proof of Theorem 2 of Burness and Tong-Viet -- 12 Degenerate Normal 2-Coverings -- 12.1 The Degenerate Normal 2-Coverings of the First Type -- 12.2 The Degenerate Normal 2-Coverings of the Second Type -- References.
• Titolo autorizzato: Normal 2-Coverings of the Finite Simple Groups and Their Generalizations
• ISBN: 9783031623486
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910874689503321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics Series