# Group Theory

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- Groups, subgroups and constructions
- Representations
- Cosets and Lagrange's theorem
- Normal subgroups and the Noether isomorphism theorems
- Cardinality identities for finite representations
- Free products and amalgamated sums
- The category of groups
- Abelian groups and the Grothendieck group of a monoid
- The action by conjugation and p-groups
- Simple groups and Sylow's theorem
- Subnormal subgroups and series
- Commutators, solvable and nilpotent groups
- Characteristic subgroups
- The symmetric group
- The Cayley graph and group actions on trees
- The Bass‒Serre theorems
- Splittings and the semidirect product
- Groups with hyperbolic Cayley graphs
- Group cohomology
- Group objects
- Groups with structure
- Topological groups

## ReferencesEdit

- Aschbacher, Finite Group Theory
- M. Artin, Algebra
- Serre, Trees