Finite groups. An introduction. (Q2811237)

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.NEWLINENEWLINE 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 \(\mathrm{GL}_n\), Chapter 10 -- Small groups.NEWLINENEWLINE Each of the chapters is followed by a series of exercises (in all about 160).