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/