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This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow's theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced 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.
List of contents
1 Linear Transformations and Linear Groups.- 2 Group Actions on Sets.- 3 Sylow's Theorems and Applications.- 4 Simple Groups.- 5 Product of Groups.- 6 Normal Series.- 7 Free Groups and Presentations.- 8 Symmetry Groups of Geometric Objects.- 9 Platonic Solids.- 10 Frieze and Wallpaper Symmetry Groups.- 11 Representations and Characters of Groups.
About the author
BIJAN DAVVAZ is Professor at the Department of Mathematics, Yazd University, Iran. He earned his Ph.D. 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. He also has served as 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. His areas of interest include algebra, algebraic hyperstructures, rough sets and fuzzy logic. On the editorial boards for 25 mathematical journals, Prof. Davvaz has authored 6 books and over 600 research papers, especially on algebra, fuzzy logic, algebraic hyperstructures and their applications.
Report
"This is an introductory book on group theory. ... There is a large number of diagrams and pictures helping the reader better understand the concepts. The many examples and worked-out exercises are the strengths of the book." (Attila Maroti, zbMATH 1526.20001, 2024)
