Missing hom and isomorphism methods between FinGenAbgroup and GAPGroup

[fingolfin]

Setup

julia> G = abelian_group([2,2])
(Z/2)^2

julia> H = symmetric_group(4);

julia> a, b = H([2,1,3,4]), H([1,2,4,3])
((1,2), (3,4))

julia> U, _ = sub(H, [a,b])
(Permutation group of degree 4, Hom: U -> H)

Then this works:

julia> hom(U, G, gens(G))
Composite map
  from permutation group of degree 4 and order 4
  to (Z/2)^2
which is the composite of
  Hom: U -> permutation group
  Map: permutation group -> (Z/2)^2 -> G

but this doesn't:

julia> hom(G, U, gens(U))
ERROR: MethodError: no method matching hom(::FinGenAbGroup, ::PermGroup, ::Vector{PermGroupElem})
The function `hom` exists, but no method is defined for this combination of argument types.

Related:

julia> is_isomorphic(H, H)
true

julia> is_isomorphic(U, H)
false

julia> is_isomorphic(G, G)
true

julia> is_isomorphic(G, U)
true

but

julia> isomorphism(H, H)   # good
Group homomorphism
  from Sym(4)
  to Sym(4)

julia> isomorphism(U, H)   # good
ERROR: ArgumentError: the groups are not isomorphic

julia> isomorphism(G, G)   # bad
ERROR: MethodError: no method matching isomorphism(::FinGenAbGroup, ::FinGenAbGroup)

julia> isomorphism(U, G)   # bad
ERROR: MethodError: no method matching isomorphism(::PermGroup, ::FinGenAbGroup)

[fingolfin]

@ThomasBreuer @mjrodgers can you please look into this?

[ThomasBreuer]

Yes, I will fix this.

[thofma]

I could add the isomorphism for FinGenAbGroup in Hecke.

[ThomasBreuer]

Thanks @thofma.
Yes, isomorphism and FinGenAbGroup belong to Hecke.
I am going to add the missing hom between FinGenAbGroup and GAPGroup (one direction) and isomorphism between FinGenAbGroup and GAPGroup (both directions) to Oscar.

[thofma]

thofma/Hecke.jl#1724