Linked from

The 11 pages that link to Free group, each with the reason it gives.

• Fundamental groupRelated: Wedges of circles have free fundamental groups, making graph examples explicit.

• Cyclic groupCompared with: A free group on multiple generators is generally far larger and less constrained than a cyclic group.

• Cayley graphRelated: Its Cayley graph is a tree, making it a basic model.

• FunctorRelated: The free-group construction extends maps of sets to homomorphisms of groups.

• Banach–Tarski paradoxNarrower topic: Rotations about two axes generate the free-group structure used to rearrange the pieces.

• Adjoint functorsBroader topic: The free-group construction is left adjoint to the functor that forgets group structure.

• Free objectBroader topic: It is the standard free object for the forgetful functor from groups to sets.

• Hausdorff paradoxRelated: Rotations about two suitably chosen axes generate the free-group structure used in the decomposition.

• Ping-pong lemmaRelated: The ping-pong conditions establish that the chosen generators satisfy no nontrivial relations.

• Tits alternativeBroader topic: The other outcome is a free subgroup on at least two generators.

• Andrews–Curtis conjectureRelated: Balanced presentations encode relators as words in a free group.