fix _as_subgroups (#4277)

and extend tests accordingly,
and fix `==` for group homomorphisms

src/Groups/homomorphisms.jl

@@ -9,7 +9,7 @@ function Base.show(io::IO, x::GAPGroupHomomorphism)
 end
 
 
-function ==(f::GAPGroupHomomorphism{S,T}, g::GAPGroupHomomorphism{S,T}) where S where T
+function ==(f::GAPGroupHomomorphism, g::GAPGroupHomomorphism)
   return GapObj(f) == GapObj(g)
 end
 

src/Groups/sub.jl

@@ -157,15 +157,7 @@ end
 
 # convert a GAP list of subgroups into a vector of Julia groups objects
 function _as_subgroups(G::T, subs::GapObj) where T <: GAPGroup
-  res = Vector{T}(undef, length(subs))
-  for i = 1:length(res)
-    res[i] = _as_subgroup_bare(G, subs[i]::GapObj)
-  end
-  return res
-end
-
-function _as_subgroups(G::PcGroup, subs::GapObj)
-  res = Vector{SubPcGroup}(undef, length(subs))
+  res = Vector{sub_type(T)}(undef, length(subs))
   for i = 1:length(res)
     res[i] = _as_subgroup_bare(G, subs[i]::GapObj)
   end

test/Groups/subgroups_and_cosets.jl

@@ -1,29 +1,41 @@
 @testset "Subgroups" begin
-   G = symmetric_group(7)
-   x = cperm(G,[1,2,3,4,5,6,7])
-   y = cperm(G,[1,2,3])
-   z = cperm(G,[1,2])
-
-   H,f=sub(G,[x,y])
-   K,g=sub(x,y)
-   @test H isa PermGroup
-   @test H==alternating_group(7)
-   @test domain(f)==H
-   @test codomain(f)==G
-   @test [f(x) for x in gens(H)]==gens(H)
-   @test (H,f)==(K,g)
-   @test is_subset(K, G)
-   flag, emb = is_subgroup(K, G)
-   @test flag
-   @test g == emb
-   @test g == embedding(K, G)
-   @test K === domain(emb)
-   @test G === codomain(emb)
-   @test is_normal_subgroup(H, G)
-   H,f=sub(G,[x,z])
-   @test H==G
-   @test f==id_hom(G)
+   S = symmetric_group(7)
+   Sx = cperm(S, [1, 2, 3, 4, 5, 6, 7])
+   Sy = cperm(S, [1, 2, 3])
+   Sz = cperm(S, [1, 2])
+
+   for T in [PermGroup, FPGroup]
+     iso = isomorphism(T, S)
+     G = codomain(iso)
+     x = iso(Sx)
+     y = iso(Sy)
+     z = iso(Sz)
+
+     H, f = sub(G, [x, y])
+     K, g = sub(x, y)
+     @test H isa Oscar.sub_type(T)
+     @test domain(f) == H
+     @test codomain(f) == G
+     @test [f(x) for x in gens(H)] == gens(H)
+     @test (H, f) == (K, g)
+     @test is_subset(K, G)
+     flag, emb = is_subgroup(K, G)
+     @test flag
+     @test g == emb
+     @test g == embedding(K, G)
+     @test K === domain(emb)
+     @test G === codomain(emb)
+     @test is_normal_subgroup(H, G)
+     H, f = sub(G, [x, z])
+     @test H == G
+     @test f == id_hom(G)
+   end
 
+   G = symmetric_group(7)
+   x = cperm(G, [1, 2, 3, 4, 5, 6, 7])
+   y = cperm(G, [1, 2, 3])
+   H, f = sub(G, [x, y])
+   @test H == alternating_group(7)
    @test !is_subset(symmetric_group(8), G)
    @test_throws ArgumentError embedding(symmetric_group(8), G)