The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

Nonfiction, Science & Nature, Mathematics, Group Theory, Algebra
Cover of the book The Maximal Subgroups of the Low-Dimensional Finite Classical Groups by John N. Bray, Derek F. Holt, Colva M. Roney-Dougal, Cambridge University Press
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Author: John N. Bray, Derek F. Holt, Colva M. Roney-Dougal ISBN: 9781107272149
Publisher: Cambridge University Press Publication: July 25, 2013
Imprint: Cambridge University Press Language: English
Author: John N. Bray, Derek F. Holt, Colva M. Roney-Dougal
ISBN: 9781107272149
Publisher: Cambridge University Press
Publication: July 25, 2013
Imprint: Cambridge University Press
Language: English

This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.

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This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.

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