# Finitely Presented Groups

Abelian GroupsAbelian group creation, generic abelian groups and elements.

[Abelian Groups](AbelianGroups/index-abelian-groups.md)Free GroupsFree group creation, subgroups and automorphisms.

[Free Groups](FreeGroups/index-free-groups.md)Introduction to FP-GroupsFP-group construction, properties and subgroups.

[Introduction to Fp-Groups](IntroductionToFPGroups/index-introduction-to-fpgroups.md)Finitely Presented GroupsFP-group construction, simplification and standard constructions.

[Finitely Presented Groups](FPGroups/index-fpgroups.md)Polycyclic GroupsPolycyclic group construction, subgroups, quotients and conversion.

[Polycyclic Groups](PolycyclicGroups/index-polycyclic-groups.md)Braid GroupsBraid group construction and element creation.

[Braid Groups](BraidGroups/index-braid-groups.md)Groups Defined by Rewrite SystemsRewriting system creation, properties and arithmetic for groups.

[Groups Defined by Rewrite Systems](GroupsDefinedByRewriteSystems/index-groups-defined-by-rewrite-systems.md)Automatic and Hyperbolic GroupsAutomatic groups and hyperbolic groups.

[Automatic and Hyperbolic Groups](AutomaticAndHyperbolicGroups/index-automatic-and-hyperbolic-groups.md)Groups of Straight-line ProgramsStraight-line program group creation and operations.

[Groups of Straight-Line Programs](GroupsOfStraightLinePrograms/index-groups-of-straight-line-programs.md)Finitely Presented SemigroupsSemigroup presentation creation, operations and properties.

[Finitely Presented Semigroups](FinitelyPresentedSemigroups/index-finitely-presented-semigroups.md)Monoids Given by Rewrite SystemsRewriting system creation, operations and homomorphisms for monoids.

[Monoids Given by Rewrite Systems](MonoidsGivenByRewriteSystems/index-monoids-given-by-rewrite-systems.md)