03449nam a22004935i 4500 978-3-031-62915-0 DE-He213 20251030112653.0 cr nn 008mamaa 240727s2024 sz | s |||| 0|eng d 9783031629150 978-3-031-62915-0 10.1007/978-3-031-62915-0 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema Korhonen, Mikko. author. aut http://id.loc.gov/vocabulary/relators/aut 81388 Maximal Solvable Subgroups of Finite Classical Groups [electronic resource] / by Mikko Korhonen. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. VIII, 298 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 2346 - 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. Group theory. 70149 Group Theory and Generalizations. 70154 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031629143 Printed edition: 9783031629167 Lecture Notes in Mathematics, 1617-9692 ; 2346 75434 https://doi.org/10.1007/978-3-031-62915-0 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 61966 61966