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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 (H77E1)
Example
GrpFPInt_Symmetric2 (H77E2)
FP-Group constructor
Example
GrpFPInt_Tetrahedral (H77E3)
Example
GrpFPInt_Modular (H77E4)
Example
GrpFPInt_Coxeter (H77E5)
Presentation Operations
Example
GrpFPInt_Simplify1 (H77E6)
Operations on Words
Presentations for Popular Groups
Example
GrpFPInt_Abelian (H77E7)
Example
GrpFPInt_Symetric (H77E8)
Constructions for FP-Groups
Example
GrpFPInt_ProductFPs (H77E9)
Example
GrpFPInt_FPGroup (H77E10)
Properties of an FP-group
Example
GrpFPInt_Perfect (H77E11)
Example
GrpFPInt_Automatic (H77E12)
Subgroups
Subgroup Constructor
Example
GrpFPInt_Subgroups1 (H77E13)
Coset Enumeration
Example
GrpFPInt_Cosets (H77E14)
Coset Action
Example
GrpFPInt_G23 (H77E15)
Enumeration of FI-Subgroups
Example
GrpFPInt_Lix1 (H77E16)
Example
GrpFPInt_Lix2 (H77E17)
Operations for FI-Subgroups
Example
GrpFPInt_Subgroups1 (H77E18)
Properties of Subgroups
Example
GrpFPInt_SubgroupPreds (H77E19)
Presentations for Subgroups
Example
GrpFPInt_Rewrite (H77E20)
Example
GrpFPInt_Rewrite2 (H77E21)
Finite FP-Groups
Example
GrpFPInt_OrderGroup (H77E22)
Example
GrpFPInt_CGraph (H77E23)
Homomorphisms of FP-Groups
Homomorphism Constructor
Example
GrpFPInt_Homomorphism (H77E24)
Searching for Homomorphisms
Example
GrpFPInt_Homomorphisms1 (H77E25)
Searching for Isomorphisms
Example
GrpFPInt_SearchForIso1 (H77E26)
Example
GrpFPInt_SearchForIso2 (H77E27)
Quotient Groups
Abelian Quotient
Example
GrpFPInt_F27 (H77E28)
Example
GrpFPInt_modular-abelian-quotient (H77E29)
p-Quotient
Example
GrpFPInt_pQuotient1 (H77E30)
Example
GrpFPInt_pQuotient2 (H77E31)
Example
GrpFPInt_pQuotient3 (H77E32)
Nilpotent Quotient
Example
GrpFPInt_NilpotentQuotient0 (H77E33)
Example
GrpFPInt_NilpotentQuotient1 (H77E34)
Example
GrpFPInt_NilpotentQuotient2 (H77E35)
Soluble Quotient
Example
GrpFPInt_SolubleQuotient1 (H77E36)
Example
GrpFPInt_SolubleQuotient2 (H77E37)
Simple Group Quotients
Example
GrpFPInt_SimpleQuotients (H77E38)
(L)
2
-Quotients
Example
GrpFPInt_L2Quotient (H77E39)
Example
GrpFPInt_L2QuotientInfinite (H77E40)
Example
GrpFPInt_L2QuotientGetMatrices (H77E41)
Bibliography
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V2.28, 28 February 2025