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Conjugacy in finite classical groups

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Conjugacy in finite classical groupsby Giovanni De Franceschi, Martin W. Liebeck, Eamonn A. O'Brien.
Author:	De Franceschi, Giovanni.
other author:	Liebeck, M. W.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xi, 176 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Finite groups.
Online resource:	https://doi.org/10.1007/978-3-031-86461-2
ISBN:	9783031864612$q(electronic bk.)

Conjugacy in finite classical groups
De Franceschi, Giovanni.

Conjugacy in finite classical groups[electronic resource] /by Giovanni De Franceschi, Martin W. Liebeck, Eamonn A. O'Brien. - Cham :Springer Nature Switzerland :2025. - xi, 176 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

- 1. Introduction and Background -- 2. General and Special Linear Groups -- 3. Preliminaries on Classical Groups -- 4. Unipotent Classes in Good Characteristic -- 5. Unipotent Classes in Bad Characteristic -- 6. Semisimple Classes -- 7. General Conjugacy Classes.

This book provides a comprehensive coverage of the theory of conjugacy in finite classical groups. Given such a classical group G, the three fundamental problems considered are the following: to list a representative for each conjugacy class of G; to describe the centralizer of each representative, by giving its group structure and a generating set; and to solve the conjugacy problem in G-namely, given two elements of G, establish whether they are conjugate, and if so, find a conjugating element. The book presents comprehensive theoretical solutions to all three problems, and uses these solutions to formulate practical algorithms. In parallel to the theoretical work, implementations of these algorithms have been developed in Magma. These form a critical component of various general algorithms in computational group theory-for example, computing character tables and solving conjugacy problems in arbitrary finite groups.

ISBN: 9783031864612$q(electronic bk.)

Standard No.: 10.1007/978-3-031-86461-2doiSubjects--Topical Terms:

245404
Finite groups.

LC Class. No.: QA171

Dewey Class. No.: 512.23

Conjugacy in finite classical groups
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245 1 0 $a Conjugacy in finite classical groups $h [electronic resource] / $c by Giovanni De Franceschi, Martin W. Liebeck, Eamonn A. O'Brien.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xi, 176 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a - 1. Introduction and Background -- 2. General and Special Linear Groups -- 3. Preliminaries on Classical Groups -- 4. Unipotent Classes in Good Characteristic -- 5. Unipotent Classes in Bad Characteristic -- 6. Semisimple Classes -- 7. General Conjugacy Classes.
520 $a This book provides a comprehensive coverage of the theory of conjugacy in finite classical groups. Given such a classical group G, the three fundamental problems considered are the following: to list a representative for each conjugacy class of G; to describe the centralizer of each representative, by giving its group structure and a generating set; and to solve the conjugacy problem in G-namely, given two elements of G, establish whether they are conjugate, and if so, find a conjugating element. The book presents comprehensive theoretical solutions to all three problems, and uses these solutions to formulate practical algorithms. In parallel to the theoretical work, implementations of these algorithms have been developed in Magma. These form a critical component of various general algorithms in computational group theory-for example, computing character tables and solving conjugacy problems in arbitrary finite groups.
650 0 $a Finite groups. $3 245404
650 1 4 $a Group Theory and Generalizations. $3 274819
700 1 $a Liebeck, M. W. $3 929643
700 1 $a O'Brien, Eamonn A. $3 991550
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u https://doi.org/10.1007/978-3-031-86461-2
950 $a Mathematics and Statistics (SpringerNature-11649)