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Conjugacy in Finite Classical Groups / by Giovanni De Franceschi, Martin W. Liebeck, Eamonn A. O'Brien

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Monographs in MathematicsPublisher: Cham : Springer Nature Switzerland, 2025Publisher: Cham : Imprint: Springer, 2025Edition: 1st ed. 2025Description: 1 Online-Ressource(XI, 176 p.)ISBN:
  • 9783031864612
Subject(s): Additional physical formats: 9783031864605 | 9783031864629 | 9783031864636 | Erscheint auch als: 9783031864605 Druck-Ausgabe | Erscheint auch als: 9783031864629 Druck-Ausgabe | Erscheint auch als: 9783031864636 Druck-AusgabeDDC classification:
  • 512.2 23
DOI: DOI: 10.1007/978-3-031-86461-2Online resources: Summary: - 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.Summary: 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.PPN: PPN: 1925486281Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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