TODO:
AUTHORS:
Bases: sage.categories.morphism.Morphism
A set-theoretic map between AbelianGroups.
Bases: sage.categories.morphism.Morphism
Some python code for wrapping GAP’s GroupHomomorphismByImages function for abelian groups. Returns “fail” if gens does not generate self or if the map does not extend to a group homomorphism, self - other.
EXAMPLES:
sage: G = AbelianGroup(3,[2,3,4],names="abc"); G
Multiplicative Abelian group isomorphic to C2 x C3 x C4
sage: a,b,c = G.gens()
sage: H = AbelianGroup(2,[2,3],names="xy"); H
Multiplicative Abelian group isomorphic to C2 x C3
sage: x,y = H.gens()
sage: from sage.groups.abelian_gps.abelian_group_morphism import AbelianGroupMorphism
sage: phi = AbelianGroupMorphism(H,G,[x,y],[a,b])
AUTHORS:
Only works for finite groups.
J must be a subgroup of G. Computes the subgroup of H which is the image of J.
EXAMPLES:
sage: G = AbelianGroup(2,[2,3],names="xy")
sage: x,y = G.gens()
sage: H = AbelianGroup(3,[2,3,4],names="abc")
sage: a,b,c = H.gens()
sage: phi = AbelianGroupMorphism(G,H,[x,y],[a,b])
Only works for finite groups.
TODO: not done yet; returns a gap object but should return a Sage group.
EXAMPLES:
sage: H = AbelianGroup(3,[2,3,4],names="abc"); H
Multiplicative Abelian group isomorphic to C2 x C3 x C4
sage: a,b,c = H.gens()
sage: G = AbelianGroup(2,[2,3],names="xy"); G
Multiplicative Abelian group isomorphic to C2 x C3
sage: x,y = G.gens()
sage: phi = AbelianGroupMorphism(G,H,[x,y],[a,b])
sage: phi.kernel()
'Group([ ])'
Bases: sage.groups.abelian_gps.abelian_group_morphism.AbelianGroupMap
Return the identity homomorphism from X to itself.
EXAMPLES:
x.__init__(...) initializes x; see help(type(x)) for signature