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Verfasst von:Korhonen, Mikko [VerfasserIn]   i
Titel:Maximal Solvable Subgroups of Finite Classical Groups
Verf.angabe:by Mikko Korhonen
Ausgabe:1st ed. 2024.
Verlagsort:Cham
 Cham
Verlag:Springer Nature Switzerland
 Imprint: Springer
E-Jahr:2024
Jahr:2024.
 2024.
Umfang:1 Online-Ressource(VIII, 298 p.)
Gesamttitel/Reihe:Lecture Notes in Mathematics ; 2346
ISBN:978-3-031-62915-0
Abstract:- Introduction -- Basic structure of maximal irreducible solvable subgroups -- Extraspecial groups -- Metrically primitive maximal irreducible solvable subgroups -- Basic properties of GB μ,ν(X1, . . . ,Xk) -- Fixed point spaces and abelian subgroups -- Maximality of the groups constructed -- Examples.
 This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan’s Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan’s classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan’s work.
DOI:doi:10.1007/978-3-031-62915-0
URL:Resolving-System: https://doi.org/10.1007/978-3-031-62915-0
 DOI: https://doi.org/10.1007/978-3-031-62915-0
Schlagwörter:(s)Auflösbare Gruppe   i / (s)Klassische Gruppe   i / (s)Maximale Untergruppe   i / (s)Klassifikation   i / (s)Primitive Permutationsgruppe   i / (s)Matrizengruppe   i / (s)Galois-Feld   i
Datenträger:Online-Ressource
Sprache:eng
Bibliogr. Hinweis:Erscheint auch als : Druck-Ausgabe
 Erscheint auch als : Druck-Ausgabe
 Erscheint auch als : Druck-Ausgabe: Korhonen, Mikko: Maximal solvable subgroups of finite classical groups. - Cham : Springer, 2024. - viii, 296 Seiten
K10plus-PPN:1896936253
Verknüpfungen:→ Übergeordnete Aufnahme
 
 
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