# Introduction to Fp-Groups

- [Introduction](introduction.md)

  - [Overview](introduction.md#overview)

  - [Definitions and Notation](introduction.md#definitions-and-notation)

- [Construction of FP-Groups](fp-group-construction.md)

  - [Relations](fp-group-construction.md#relations)

  - [Quotient Group Constructors](fp-group-construction.md#quotient-group-constructors)

    - [`Example: Symmetric1`](fp-group-construction.md#example-ex-755b4c)

    - [`Example: Symmetric2`](fp-group-construction.md#example-ex-17dd50)

  - [FP-Group constructor](fp-group-construction.md#fp-group-constructor)

    - [`Example: Tetrahedral`](fp-group-construction.md#example-ex-20a432)

    - [`Example: Modular`](fp-group-construction.md#example-ex-a5e77e)

    - [`Example: Coxeter`](fp-group-construction.md#example-ex-17488a)

  - [Presentation Operations](fp-group-construction.md#presentation-operations)

    - [`Example: Simplify1`](fp-group-construction.md#example-ex-c32ec7)

  - [Operations on Words](fp-group-construction.md#operations-on-words)

  - [Presentations for Popular Groups](fp-group-construction.md#presentations-for-popular-groups)

    - [`Example: Abelian`](fp-group-construction.md#example-ex-318133)

    - [`Example: Symetric`](fp-group-construction.md#example-ex-169352)

  - [Constructions for FP-Groups](fp-group-construction.md#constructions-for-fp-groups)

    - [`Example: Product F Ps`](fp-group-construction.md#example-ex-7dc82f)

    - [`Example: FP Group`](fp-group-construction.md#example-ex-c105bf)

- [Properties of an FP-group](Properties.md)

  - [`Example: Perfect`](Properties.md#example-ex-5d2db4)

  - [`Example: Automatic`](Properties.md#example-ex-52e6c5)

- [Subgroups](subgroup-general.md)

  - [Subgroup Constructor](subgroup-general.md#subgroup-constructor)

    - [`Example: Subgroups1`](subgroup-general.md#example-ex-7c2095)

  - [Coset Enumeration](subgroup-general.md#coset-enumeration)

    - [`Example: Cosets`](subgroup-general.md#example-ex-476bb1)

  - [Coset Action](subgroup-general.md#coset-action)

    - [`Example: G23`](subgroup-general.md#example-ex-6c4e10)

  - [Enumeration of FI-Subgroups](subgroup-general.md#enumeration-of-fi-subgroups)

    - [`Example: Lix1`](subgroup-general.md#example-ex-c69596)

    - [`Example: Lix2`](subgroup-general.md#example-ex-c3d6e8)

  - [Operations for FI-Subgroups](subgroup-general.md#operations-for-fi-subgroups)

    - [`Example: Subgroups1`](subgroup-general.md#example-ex-f46c39)

  - [Properties of Subgroups](subgroup-general.md#properties-of-subgroups)

    - [`Example: Subgroup Preds`](subgroup-general.md#example-ex-b1118e)

  - [Presentations for Subgroups](subgroup-general.md#presentations-for-subgroups)

    - [`Example: Rewrite`](subgroup-general.md#example-ex-d4d467)

    - [`Example: Rewrite2`](subgroup-general.md#example-ex-282060)

- [Finite FP-Groups](Finite.md)

  - [`Example: Order Group`](Finite.md#example-ex-fb0cc3)

  - [`Example: C Graph`](Finite.md#example-ex-19bd36)

- [Homomorphisms of FP-Groups](homomorphism.md)

  - [Homomorphism Constructor](homomorphism.md#homomorphism-constructor)

    - [`Example: Homomorphism`](homomorphism.md#example-ex-1337d3)

  - [Searching for Homomorphisms](homomorphism.md#searching-for-homomorphisms)

    - [`Example: Homomorphisms1`](homomorphism.md#example-ex-1803a5)

  - [Searching for Isomorphisms](homomorphism.md#searching-for-isomorphisms)

    - [`Example: Search For Iso1`](homomorphism.md#example-ex-cebd96)

    - [`Example: Search For Iso2`](homomorphism.md#example-ex-8e44ee)

- [Quotient Groups](quotient.md)

  - [Abelian Quotient](quotient.md#abelian-quotient)

    - [`Example: F27`](quotient.md#example-ex-12a8db)

    - [`Example: Modular Abelian Quotient`](quotient.md#example-ex-26e129)

  - [$p$-Quotient](quotient.md#p-quotient)

    - [`Example: p Quotient1`](quotient.md#example-ex-81ff16)

    - [`Example: p Quotient2`](quotient.md#example-ex-94855c)

    - [`Example: p Quotient3`](quotient.md#example-ex-e48428)

  - [Nilpotent Quotient](quotient.md#nilpotent-quotient)

    - [`Example: Nilpotent Quotient0`](quotient.md#example-ex-0b5725)

    - [`Example: Nilpotent Quotient1`](quotient.md#example-ex-470660)

    - [`Example: Nilpotent Quotient2`](quotient.md#example-ex-f4b49e)

  - [Soluble Quotient](quotient.md#soluble-quotient)

    - [`Example: Soluble Quotient1`](quotient.md#example-ex-211a7e)

    - [`Example: Soluble Quotient2`](quotient.md#example-ex-820eb8)

  - [Simple Group Quotients](quotient.md#simple-group-quotients)

    - [`Example: Simple Quotients`](quotient.md#example-ex-af2186)

  - [${\rm L}_2$-Quotients](quotient.md#rm-l-2-quotients)

    - [`Example: L2Quotient`](quotient.md#example-ex-5313fb)

    - [`Example: L2Quotient Infinite`](quotient.md#example-ex-0eaade)

    - [`Example: L2Quotient Get Matrices`](quotient.md#example-ex-ba85d0)