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Magma
Computer • algebra
Documentation
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group
AbelianBasis(G) : GrpMat -> [ GrpMatElt ], [ RngIntElt ]
Abelian Group Functions (MATRIX GROUPS OVER GENERAL RINGS)
Abstract Group Predicates (GROUPS)
Abstract Group Predicates (MATRIX GROUPS OVER GENERAL RINGS)
Abstract Properties of a Group (PERMUTATION GROUPS)
Accessing the ATLAS Groups (DATABASES OF GROUPS)
Action of PSL
2
(R) on the Upper Half Plane (CONGRUENCE SUBGROUPS OF PSL
2
(R))
ALMOST SIMPLE GROUPS
Automatic Groups of 3-Manifolds (DATABASES OF GROUPS)
Automorphism Group (ALGEBRAIC FUNCTION FIELDS)
Automorphism Group (FINITE SOLUBLE GROUPS)
Automorphism Group (LINEAR CODES OVER FINITE FIELDS)
Automorphism Group of a Graph or Digraph (GRAPHS)
Automorphism Groups (LINEAR CODES OVER FINITE FIELDS)
Basic Group Properties (FINITE SOLUBLE GROUPS)
Braid Groups (COXETER GROUPS)
Class Group and Unit Group (NUMBER FIELDS)
Class Group Internals (NUMBER FIELDS AND ORDERS)
Class Group Map Caching (NUMBER FIELDS AND ORDERS)
Class Groups (BINARY QUADRATIC FORMS)
Construction from Groups, Codes and Designs (GRAPHS)
Construction of a General Matrix Group (MATRIX GROUPS OVER GENERAL RINGS)
Construction of an FP-Group (FINITELY PRESENTED GROUPS)
Construction of Finite Complex Reflection Groups (REFLECTION GROUPS)
Construction of FP-Groups (INTRODUCTION TO FP-GROUPS [FINITELY-PRESENTED GROUPS])
Construction of Real Reflection Groups (REFLECTION GROUPS)
Construction of Reflection Groups (REFLECTION GROUPS)
Construction of Standard Groups (POLYCYCLIC GROUPS)
Conversion to FP-Groups (FINITELY PRESENTED GROUPS)
Creation of a Matrix Group (MATRIX GROUPS OVER GENERAL RINGS)
Divisor Group (ALGEBRAIC CURVES)
Divisor Group (TORIC VARIETIES)
Finite Group Cohomology (COHOMOLOGY AND EXTENSIONS)
FP-Group constructor (INTRODUCTION TO FP-GROUPS [FINITELY-PRESENTED GROUPS])
Functions related to Divisor Class Groups of Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
General Group Properties (ABELIAN GROUPS)
General Group Properties (POLYCYCLIC GROUPS)
General Soluble Group (FINITE SOLUBLE GROUPS)
Generators and Relations (PERMUTATION GROUPS)
Graphs Constructed from Groups (GRAPHS)
Group Actions (LINEAR CODES OVER FINITE FIELDS)
Group Actions on Polynomials (INVARIANT THEORY)
Group Algebras (ALGEBRAS WITH INVOLUTION)
Group Order (MATRIX GROUPS OVER GENERAL RINGS)
Group Order (PERMUTATION GROUPS)
Group Recognition (ALMOST SIMPLE GROUPS)
Group Theoretic Functions (CLASS FIELD THEORY)
GROUPS
Ideal Class Group (QUADRATIC FIELDS)
Ideal Class Groups (NUMBER FIELDS AND ORDERS)
Introduction (FINITELY PRESENTED GROUPS)
Lifting Algorithm (FINITE SOLUBLE GROUPS)
Lifting from the Automorphism Group of a Sylow p-subgroup (FINITE SOLUBLE GROUPS)
Linear Equivalence and Class Group (ALGEBRAIC CURVES)
MATRIX GROUPS OVER INFINITE FIELDS
MATRIX GROUPS OVER Q AND Z
Norm Group (p-ADIC RINGS AND THEIR EXTENSIONS)
Operations on Coxeter Groups (COXETER GROUPS)
Operations on Elements (COXETER GROUPS)
p-group (FINITE SOLUBLE GROUPS)
p-group Functions (MATRIX GROUPS OVER GENERAL RINGS)
Permutation Representations of Linear Groups (PERMUTATION GROUPS)
Permutations as Words (PERMUTATION GROUPS)
Power Groups (POLYCYCLIC GROUPS)
PowerGroup (FINITE SOLUBLE GROUPS)
Properties of an FP-Group (FINITELY PRESENTED GROUPS)
Properties of Coxeter Groups (COXETER GROUPS)
Quotient Group Constructor (FINITELY PRESENTED GROUPS)
Quotient Group Constructors (INTRODUCTION TO FP-GROUPS [FINITELY-PRESENTED GROUPS])
Ray Class Groups (CLASS FIELD THEORY)
Recognition Of Classical Groups in Low Degree (ALMOST SIMPLE GROUPS)
Selmer Groups (CLASS FIELD THEORY)
Setting the Class Group Bounds (NUMBER FIELDS AND ORDERS)
Simplifying Automorphism Group Computations (MULTILINEAR ALGEBRA)
Soluble Matrix Groups (MATRIX GROUPS OVER GENERAL RINGS)
Standard Groups and Extensions (GROUPS)
Structure Operations (FINITE SOLUBLE GROUPS)
Task Group Management (PARALLELISM)
The 2-Selmer Group (HYPERELLIPTIC CURVES)
The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
The Collineation Group of a Plane (FINITE PLANES)
The FP-Group Constructor (FINITELY PRESENTED GROUPS)
The Mordell--Weil Group (ELLIPTIC CURVES OVER FUNCTION FIELDS)
The Mordell-Weil Group (HYPERELLIPTIC CURVES)
The Unit Group (INTEGER RESIDUE CLASS RINGS)
Unit Group (p-ADIC RINGS AND THEIR EXTENSIONS)
Unit Groups (NUMBER FIELDS AND ORDERS)
Units and Unit Groups (QUATERNION ALGEBRAS)
W-graphs (COXETER GROUPS)
Contents
Index (g)
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V2.28, 13 July 2023