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Magma
Computer • algebra
Documentation
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Introduction
Overview
Definitions and Notation
Construction of FP-Groups
Relations
Quotient Group Constructors
Example
GrpFPInt_Symmetric1 (H79E1)
Example
GrpFPInt_Symmetric2 (H79E2)
FP-Group constructor
Example
GrpFPInt_Tetrahedral (H79E3)
Example
GrpFPInt_Modular (H79E4)
Example
GrpFPInt_Coxeter (H79E5)
Presentation Operations
Example
GrpFPInt_Simplify1 (H79E6)
Operations on Words
Presentations for Popular Groups
Example
GrpFPInt_Abelian (H79E7)
Example
GrpFPInt_Symetric (H79E8)
Constructions for FP-Groups
Example
GrpFPInt_ProductFPs (H79E9)
Example
GrpFPInt_FPGroup (H79E10)
Properties of an FP-group
Example
GrpFPInt_Perfect (H79E11)
Example
GrpFPInt_Automatic (H79E12)
Subgroups
Subgroup Constructor
Example
GrpFPInt_Subgroups1 (H79E13)
Coset Enumeration
Example
GrpFPInt_Cosets (H79E14)
Coset Action
Example
GrpFPInt_G23 (H79E15)
Enumeration of FI-Subgroups
Example
GrpFPInt_Lix1 (H79E16)
Example
GrpFPInt_Lix2 (H79E17)
Operations for FI-Subgroups
Example
GrpFPInt_Subgroups1 (H79E18)
Properties of Subgroups
Example
GrpFPInt_SubgroupPreds (H79E19)
Presentations for Subgroups
Example
GrpFPInt_Rewrite (H79E20)
Example
GrpFPInt_Rewrite2 (H79E21)
Finite FP-Groups
Example
GrpFPInt_OrderGroup (H79E22)
Example
GrpFPInt_CGraph (H79E23)
Homomorphisms of FP-Groups
Homomorphism Constructor
Example
GrpFPInt_Homomorphism (H79E24)
Searching for Homomorphisms
Example
GrpFPInt_Homomorphisms1 (H79E25)
Searching for Isomorphisms
Example
GrpFPInt_SearchForIso1 (H79E26)
Example
GrpFPInt_SearchForIso2 (H79E27)
Quotient Groups
Abelian Quotient
Example
GrpFPInt_F27 (H79E28)
Example
GrpFPInt_modular-abelian-quotient (H79E29)
p-Quotient
Example
GrpFPInt_pQuotient1 (H79E30)
Example
GrpFPInt_pQuotient2 (H79E31)
Example
GrpFPInt_pQuotient3 (H79E32)
Nilpotent Quotient
Example
GrpFPInt_NilpotentQuotient0 (H79E33)
Example
GrpFPInt_NilpotentQuotient1 (H79E34)
Example
GrpFPInt_NilpotentQuotient2 (H79E35)
Soluble Quotient
Example
GrpFPInt_SolubleQuotient1 (H79E36)
Example
GrpFPInt_SolubleQuotient2 (H79E37)
Simple Group Quotients
Example
GrpFPInt_SimpleQuotients (H79E38)
(L)
2
-Quotients
Example
GrpFPInt_L2Quotient (H79E39)
Example
GrpFPInt_L2QuotientInfinite (H79E40)
Example
GrpFPInt_L2QuotientGetMatrices (H79E41)
Bibliography
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V2.29, 21 October 2025