國立高雄大學圖資館 |

登入

回首頁

Maximal solvable subgroups of finite classical groups

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Maximal solvable subgroups of finite classical groupsby Mikko Korhonen.
作者:	Korhonen, Mikko.
出版者:	Cham :Springer Nature Switzerland :2024.
面頁冊數:	viii, 298 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Solvable groups.
電子資源:	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
LDR:02404nmm a2200325 a 4500 001 667240
003 DE-He213
005 20240727125246.0
006 m d
007 cr nn 008maaau
008 250107s2024 sz s 0 eng d
020 $a 9783031629150$q(electronic bk.)
020 $a 9783031629143$q(paper)
024 7 $a 10.1007/978-3-031-62915-0 $2 doi
035 $a 978-3-031-62915-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA177
072 7 $a PBG $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBG $2 thema
082 0 4 $a 512.23 $2 23
090 $a QA177 $b .K84 2024
100 1 $a Korhonen, Mikko. $3 980059
245 1 0 $a Maximal solvable subgroups of finite classical groups $h [electronic resource] / $c by Mikko Korhonen.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a viii, 298 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2346
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.
650 0 $a Solvable groups. $3 272032
650 0 $a Finite groups. $3 245404
650 1 4 $a Group Theory and Generalizations. $3 274819
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-62915-0
950 $a Mathematics and Statistics (SpringerNature-11649)