A First Course in Group Theory - Davvaz, Bijan

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Résumé :
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange?s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.

Biographie:
Bijan Davvaz is Professor at the Department of Mathematical Sciences, Yazd University, Iran. He also has served as the Head of the Department of Mathematics (1998-2002), Chairman of the Faculty of Science (2004-2006) and Vice-President for Research (2006-2008) at Yazd University, Iran. He earned his PhD in Mathematics with a thesis on Topics in Algebraic Hyperstructures from Tarbiat Modarres University, Iran, and completed his M.Sc. in Mathematics from the University of Tehran, Iran. His areas of interest include algebra, algebraic hyperstructures, rough sets and fuzzy logic. On the editorial boards of 25 mathematical journals, Prof. Davvaz has contributed more than 700 research papers on algebra, fuzzy logic and algebraic hyperstructures. He also has authored eight books including three with Springer: Examples and Problems in Advanced Calculus: Real-Valued Functions, Groups and Symmetry: Theory and Applications and A First Course in Group Theory....

Sommaire:

Preliminaries Notions.- Symmetries of Shapes.- Binary Operations.- Cyclic Groups.- Inverse Functions and Permutations.- Group of Arithmetical Functions.- Matrix Groups.- Translation and Scaling Matrices.- Cosets of Subgroups and Lagrange?s Theorem.- Normal Subgroups and Factor Groups.- Some Special Subgroups.- Commutators and Derived Subgroups.- Maximal Subgroups.- Group Homomorphisms.- Homomorphisms and Their Properties.- Cayley?s Theorem.- Another View of Linear Groups.