Group Theory

Decorative picture.

Group Theory

Table of Contents

• 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

References

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