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

Abelian 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

Permutation Groups

• 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

Matrix and Affine Groups

• 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

Lie Groups

• Nilpotent Lie groups

Partition Refinement

• 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

Internals

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

Indices and Tables

• Index

• Module Index

• Search Page