A First Course in Group Theory

Bijan Davvaz (Autor)

Buch | Softcover

291 Seiten

2022 | 1st ed. 2021
Springer Verlag, Singapore
978-981-16-6367-3 (ISBN)

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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. 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.

Bijan Davvaz is Professor at the Department of Mathematics, Yazd University, Iran. Earlier, he 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 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. 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.

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.

Erscheinungsdatum	16.11.2022
Zusatzinfo	79 Illustrations, color; 4 Illustrations, black and white; XV, 291 p. 83 illus., 79 illus. in color.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Algebraic Structures • combinatorics • factor groups • Groups of Geometric Objects • group theory • homomorphisms • Lagrange’s Theorem • Normal subgroups • Number Theory • permutation groups • Representation • set theory • sylow theorems • symmetry • Wallpaper Symmetry Groups
ISBN-10	981-16-6367-X / 981166367X
ISBN-13	978-981-16-6367-3 / 9789811663673
Zustand	Neuware