A First Course in Group Theory
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ISBN-13:
9789811663642
Veröffentl:
2021
Einband:
HC runder Rücken kaschiert
Erscheinungsdatum:
11.11.2021
Seiten:
308
Autor:
Bijan Davvaz
Gewicht:
629 g
Format:
241x160x23 mm
Sprache:
Englisch
Beschreibung:
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.
Discusses group theory from theoretical as well as geometrical point of view
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.
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