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Maximal solvable subgroups of finite classical groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Maximal solvable subgroups of finite classical groupsby Mikko Korhonen.
Author:	Korhonen, Mikko.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	viii, 298 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Solvable groups.
Online resource:	https://doi.org/10.1007/978-3-031-62915-0
ISBN:	9783031629150$q(electronic bk.)

Maximal solvable subgroups of finite classical groups
Korhonen, Mikko.

Maximal solvable subgroups of finite classical groups[electronic resource] /by Mikko Korhonen. - Cham :Springer Nature Switzerland :2024. - viii, 298 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23461617-9692 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783031629150$q(electronic bk.)

Standard No.: 10.1007/978-3-031-62915-0doiSubjects--Topical Terms:

272032
Solvable groups.

LC Class. No.: QA177

Dewey Class. No.: 512.23

Maximal solvable subgroups of finite classical groups
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520 $a 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.
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