Normal 2-Coverings of the Finite Simple Groups and their Generalizations
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Beschreibung
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,
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,
Provides the first comprehensive classification of normal 2-coverings of non-abelian simple groups The first reference book to collect and consolidate existing research on normal 2-coverings and their applications Showcases a wide range of applications of normal 2-coverings across different mathematical domains
Autor*in
Daniela Bubboloni
Themen in »Normal 2-Coverings of the Finite Simple Groups and their Generalizations«
Normal 2-Covering Simple Group Derangement Conjugacy Class Maximal Subgroup Kronecker Class
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“This monograph will be of interest to anyone interested in finite simple groups. Beginners will find much useful information beyond the main result, such as methods for working with classical groups, Singer cycles in matrix groups, primitive prime divisors, and much more.” (A. M. Staroletov, Mathematical Reviews, March, 2026)
“The purpose of this monograph is the classification of finite non-abelian simple groups ... . the authors give various motivations for their investigation. Besides the intrinsic theoretical interest in (weak) normal 2-coverings, a few remarkable applications have arisen ... . Each of these applications has a number of interesting open questions and conjectures ... . The reviewer believes that the presence of a subject index ... would have greatly aided the scholar in reading this interesting work.” (Enrico Jabara, zbMATH 1548.20003, 2024)
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