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Sage 10.3 Reference Manual

Home - Groups

Examples of Groups
Base class for groups
Group homomorphisms for groups with a GAP backend
LibGAP-based Groups
Generic LibGAP-based Group
Mix-in Class for GAP-based Groups
PARI Groups
Miscellaneous generic functions
Free Groups
Finitely Presented Groups
Named Finitely Presented Groups
Braid groups
Cubic Braid Groups
Indexed Free Groups
Artin Groups
Right-Angled Artin Groups
Cactus Groups
Functor that converts a commutative additive group into a multiplicative group.
Semidirect product of groups
Miscellaneous Groups
Semimonomial transformation group
Elements of a semimonomial transformation group
Kernel Subgroups
Class functions of groups.
Conjugacy classes of groups

Multiplicative Abelian Groups
Finitely generated abelian groups with GAP.
Automorphisms of abelian groups
Multiplicative Abelian Groups With Values
Dual groups of Finite Multiplicative Abelian Groups
Base class for abelian group elements
Abelian group elements
Elements (characters) of the dual group of a finite Abelian group
Homomorphisms of abelian groups
Additive Abelian Groups
Wrapper class for abelian groups
Groups of elements representing (complex) arguments.
Groups of imaginary elements

Catalog of permutation groups
Constructor for permutations
Permutation groups
“Named” Permutation groups (such as the symmetric group, S_n)
Permutation group elements
Permutation group homomorphisms
Rubik’s cube group functions
Conjugacy Classes Of The Symmetric Group

Library of Interesting Groups
Base classes for Matrix Groups
Matrix group over a ring that GAP understands
Matrix Group Elements
Matrix group elements implemented in GAP
Finitely Generated Matrix Groups
Finitely Generated Matrix Groups with GAP
Homomorphisms Between Matrix Groups
Matrix Group Homsets
Binary Dihedral Groups
Coxeter Groups As Matrix Groups
Linear Groups
Linear Groups with GAP
Orthogonal Linear Groups
Orthogonal Linear Groups with GAP
Groups of isometries
Symplectic Linear Groups
Symplectic Linear Groups with GAP
Unitary Groups \(GU(n,q)\) and \(SU(n,q)\)
Unitary Groups \(GU(n,q)\) and \(SU(n,q)\) with GAP
Heisenberg Group
Affine Groups
Euclidean Groups
Elements of Affine Groups

Nilpotent Lie groups

Canonical augmentation
Data structures
Graph-theoretic partition backtrack functions
Partition backtrack functions for lists – a simple example of using partn_ref
Partition backtrack functions for matrices

Base for Classical Matrix Groups
Base for Classical Matrix Groups with GAP

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Library of Interesting Groups#

Type groups.matrix.<tab> to access examples of groups implemented as permutation groups.

Base classes for Matrix Groups

Conjugacy Classes Of The Symmetric Group

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