Package sage :: Package groups :: Package perm_gps :: Module permgroup_morphism

Module permgroup_morphism


Permutation group homomorphisms

AUTHOR:
    - David Joyner (2006-03-21): first version
    - David Joyner (2008-06): fixed kernel and image to return a group,
                              instead of a string.

EXAMPLES:
    sage: G = CyclicPermutationGroup(4)
    sage: gens = G.gens()
    sage: H = DihedralGroup(4)
    sage: g = G([(1,2,3,4)])
    sage: phi = PermutationGroupMorphism_im_gens( G, H, gens, gens)
    sage: phi.image(G)
    Permutation Group with generators [(1,2,3,4)]
    sage: phi.kernel()
    Permutation Group with generators [()]
    sage: phi.image(g)                  
    (1,2,3,4)
    sage: phi(g)                        
    (1,2,3,4)
    sage: phi.range()
    Dihedral group of order 8 as a permutation group
    sage: phi.codomain()
    Dihedral group of order 8 as a permutation group
    sage: phi.domain()
    Cyclic group of order 4 as a permutation group

Classes

[hide private]

PermutationGroupMap
A set-theoretic map between PermutationGroups.

PermutationGroupMorphism_id
TODO: NOT FINISHED YET!! Return the identity homomorphism from X to itself.

PermutationGroupMorphism_from_gap
This is a Python trick to allow SAGE programmers to create a group homomorphism using GAP using very general constructions.

PermutationGroupMorphism_im_gens
Some python code for wrapping GAP's GroupHomomorphismByImages function but only for permutation groups.

PermutationGroupMorphism
Some python code for wrapping GAP's GroupHomomorphismByImages function but only for permutation groups.

Functions

[hide private]

gap_format(x)
Put a permutation in Gap format, as a string.

source code

is_PermutationGroupMorphism(f)

source code