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Magma
Computer • algebra
Documentation
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groups
Accessing Information (BRAID GROUPS)
Arithmetic Operators and Functions for Elements (BRAID GROUPS)
Attributes of Dirichlet Groups (INTEGER RESIDUE CLASS RINGS)
Automatic Conversions (BRAID GROUPS)
Automatic Groups (AUTOMATIC AND HYPERBOLIC GROUPS)
Automorphism Groups (FINITE SOLUBLE GROUPS)
Boolean Predicates for Elements (BRAID GROUPS)
Building Permutation Groups (PERMUTATION GROUPS)
Calculating Cohomology (COHOMOLOGY AND EXTENSIONS)
Computing Class Invariants Interactively (BRAID GROUPS)
Computing Minimal Simple Elements (BRAID GROUPS)
Computing Normal Forms of Elements (BRAID GROUPS)
Computing the Class Invariants (BRAID GROUPS)
Conjugacy in Classical Groups (MATRIX GROUPS OVER GENERAL RINGS)
Conjugacy Testing and Conjugacy Search (BRAID GROUPS)
Conjugacy Testing and Conjugacy Search (BRAID GROUPS)
Constructing and Accessing Braid Groups (BRAID GROUPS)
Coxeter and Reflection Groups (INTRODUCTION TO LIE THEORY [LIE THEORY])
COXETER GROUPS
Creating Elements of a Braid Group (BRAID GROUPS)
Creation of Gamma-groups (COHOMOLOGY AND EXTENSIONS)
Default Presentations (BRAID GROUPS)
Definition of the Class Invariants (BRAID GROUPS)
Distinguishing Groups (MULTILINEAR ALGEBRA)
Exceptional Groups (ALMOST SIMPLE GROUPS)
Finite FP-Groups (FINITELY PRESENTED GROUPS)
Functions on Groups and Group Elements (DIRICHLET AND HECKE CHARACTERS)
Generating p-groups (FINITE SOLUBLE GROUPS)
Generic Groups (CLASS FIELD THEORY)
Group Algebras of p-groups (BASIC ALGEBRAS)
GROUPS OF LIE TYPE
Hyperbolic Groups (AUTOMATIC AND HYPERBOLIC GROUPS)
Introduction (BRAID GROUPS)
Introduction (POLYCYCLIC GROUPS)
Invariants of Conjugacy Classes (BRAID GROUPS)
Lattice Operations (BRAID GROUPS)
Lattice Structure and Simple Elements (BRAID GROUPS)
Mixed Canonical Form and Lattice Operations (BRAID GROUPS)
Normal Form for Elements of a Braid Group (BRAID GROUPS)
Polycyclic Groups and Polycyclic Presentations (POLYCYCLIC GROUPS)
Printing of Elements (BRAID GROUPS)
Properties of Finite Groups Of Lie Type (ALMOST SIMPLE GROUPS)
Ray Class Groups (CLASS FIELD THEORY FOR GLOBAL FUNCTION FIELDS)
Representation Used for Group Operations (BRAID GROUPS)
Representing Elements of a Braid Group (BRAID GROUPS)
Structure of Congruence Subgroups (CONGRUENCE SUBGROUPS OF PSL
2
(R))
Task Groups (PARALLELISM)
The p-groups of Order Dividing p
7
(DATABASES OF GROUPS)
Triangle Groups (ARITHMETIC FUCHSIAN GROUPS AND SHIMURA CURVES)
Working with Elements of a Braid Group (BRAID GROUPS)
groups-elements
Functions on Groups and Group Elements (DIRICHLET AND HECKE CHARACTERS)
groups-lie-type
TwistedRowReductionMap(ρ) : Map[GrpLie,GrpMat] -> UserProgram
GROUPS OF LIE TYPE
Groups4
Groups4P(o) : RngIntElt -> List
NumberOfGroups4P(o) : RngIntElt -> RngIntElt
Groups4P
Groups4P(o) : RngIntElt -> List
GroupToRoot
GrpCox_GroupToRoot (Example H105E7)
Growth
GrowthFunction(G) : GrpAtc -> FldFunRatElt
growth
The Growth Function (AUTOMATIC AND HYPERBOLIC GROUPS)
growth-function
The Growth Function (AUTOMATIC AND HYPERBOLIC GROUPS)
GrowthFunction
GrowthFunction(G) : GrpAtc -> FldFunRatElt
GrpAtc_GrowthFunction (Example H82E10)
grp
AUTOMORPHISM GROUPS
Groups of Lie Type (REPRESENTATIONS OF LIE GROUPS AND ALGEBRAS)
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
Transfer from GrpPC (FINITE SOLUBLE GROUPS)
Transfer to GrpPC (FINITE SOLUBLE GROUPS)
grp-alg-ops
BaseRing(A) : AlgGrp -> Rng
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
grp-auto
AUTOMORPHISM GROUPS
grp-burnsidecokernel
Grp_grp-burnsidecokernel (Example H63E29)
grp-group
Grp_grp-group (Example H63E18)
grp-groupname
Grp_grp-groupname (Example H63E17)
grp-ishyperelementary
Grp_grp-ishyperelementary (Example H63E23)
grp-ispermutationcharacter
Chtr_grp-ispermutationcharacter (Example H98E3)
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V2.28, 13 July 2023