#group-theory

20. Group Theory and Generalizations

This volume studies groups as algebraic structures encoding symmetry. It develops structural, combinatorial, and computational aspects, along with generalizations such as group actions and extensions. Part I. Foundations of Group Theory Chapter 1. Groups 1.1 Definitions and examples 1.2 Subgroups 1.3 Cyclic groups 1.4 Permutation groups 1.5 Basic properties Chapter 2. Homomorphisms 2.1 Group homomorphisms 2.2 Kernels and images 2.3 Isomorphism theorems 2.4 Automorphisms 2.5 Examples Chapter 3. Cosets and...