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Conjugacy in finite classical groups

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Conjugacy in finite classical groupsby Giovanni De Franceschi, Martin W. Liebeck, Eamonn A. O'Brien.
作者:	De Franceschi, Giovanni.
其他作者:	Liebeck, M. W.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xi, 176 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Finite groups.
電子資源:	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

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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.
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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
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