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20-01 Group theory and generalizations -- Instructional exposition (textbooks, tutorial papers, etc.)

20C15 Group theory and generalizations -- Representation theory of groups -- Ordinary representations and characters

20J06 Group theory and generalizations -- Connections with homological algebra and category theory -- Cohomology of groups En-ligne: Zentralblatt | MSN

Location | Call Number | Status | Date Due |
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Salle R | 03912-01 / 20 SER (Browse Shelf) | Available |

Version anglaise d'un cours donné à l'Ecole Normale Supérieure de Jeunes Filles, Paris, 1978-1979

Bibliogr. p. 164-169. Index

Finite group theory is remarkable for the simplicity of its statements and the difficulty of their proofs. It is essential in several branches of mathematics, notably number theory. This book is an elementary textbook on the finite group theory for students and general readers. Written by the eminent French mathematician Jean-Pierre Serre (a principal contributor to algebraic topology, algebraic geometry, group theory, and number theory, awarded by the Fields Medal in 1954 and by the first Abel Prize in 2003), this brand-new textbook is based upon a course given by Serre at École Normale Supérieure de Jeunes Filles, Paris in 1978-1979.

The contents of the ten chapters are following. Chapter 1 – Preliminaries, Chapter 2 – Sylow theorems, Chapter 3 – Solvable groups and nilpotent groups, Chapter 4 – Group extensions, Chapter 5 – Hall subgroups, Chapter 6 – Frobenius groups, Chapter 7 – Transfer, Chapter 8 – Characters, Chapter 9 – Finite subgroups of GLn , Chapter 10 – Small groups.

Each of the chapters is followed by a series of exercises (in all about 160). (zbMath)

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