Free Groups: Introduction and Examples

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Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Coxeter Groups: Generators and Relations

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Group Actions and Fundamental Groups

Delves into group actions, coverings, fundamental groups, and homomorphisms in topological spaces.

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Group Theory: Combinatorial Approach

Covers group theory with a focus on group presentations and subgroup generation.

Abelian Groups: Free Abelian Groups

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Free Abelian Groups and Homomorphisms

Explores free abelian groups, homomorphisms, and exact sequences in the context of different categories.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Endomorphisms and automorphisms of totally disconnected locally compact groups

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing the properties of flat groups and free abelian subgroups.