First Course in Group Theory

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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• Álgebra
• Grupos e teoria do grupo
• Teoria dos números

Group Theory;Symmetry;Permutation Groups;Representation;Sylow Theorems;Groups of Geometric Objects;Wallpaper Symmetry Groups;Set Theory;Combinatorics;Number Theory;Algebraic Structures;Lagrange's Theorem;Normal Subgroups;Factor Groups;Homomorphisms