From 0012b969fa430178dc265d9fa4fce1c99a434ef8 Mon Sep 17 00:00:00 2001
From: Thomas Breuer <sam@math.rwth-aachen.de>
Date: Fri, 12 Apr 2024 09:24:52 +0200
Subject: [PATCH] fix a problem with `isomorphism` for trivial groups (#3586)

---
 experimental/GModule/Cohomology.jl    |  7 ++++---
 experimental/GModule/test/runtests.jl |  4 ++++
 src/Groups/homomorphisms.jl           | 12 ++++++++++--
 test/Groups/homomorphisms.jl          |  2 ++
 4 files changed, 20 insertions(+), 5 deletions(-)

diff --git a/experimental/GModule/Cohomology.jl b/experimental/GModule/Cohomology.jl
index aa32aae0ae39..c8fb1964a33f 100644
--- a/experimental/GModule/Cohomology.jl
+++ b/experimental/GModule/Cohomology.jl
@@ -184,11 +184,12 @@ end
 function fp_group_with_isomorphism(C::GModule)
   #TODO: better for PcGroup!!!
   if !isdefined(C, :F)
-    if (!isa(group(C), FPGroup)) && is_trivial(group(C))
+    G = group(C)
+    if (!isa(G, FPGroup)) && is_trivial(G)
       C.F = free_group(0)
-      C.mF = hom(group(C), C.F, gens(group(C)), elem_type(C.F)[])
+      C.mF = hom(G, C.F, elem_type(G)[], elem_type(C.F)[])
     else
-      C.F, C.mF = fp_group_with_isomorphism(gens(group(C)))
+      C.F, C.mF = fp_group_with_isomorphism(gens(G))
     end
   end
   return C.F, C.mF
diff --git a/experimental/GModule/test/runtests.jl b/experimental/GModule/test/runtests.jl
index c379e59525ff..5697809cc3e1 100644
--- a/experimental/GModule/test/runtests.jl
+++ b/experimental/GModule/test/runtests.jl
@@ -24,6 +24,10 @@ end
 
 
 @testset "Experimental.gmodule" begin
+  G = small_group(1, 1)
+  z = Oscar.RepPc.reps(QQ, G)
+  _, mp = Oscar.GrpCoh.fp_group_with_isomorphism(z[1])
+  @test is_bijective(mp)
 
   G = small_group(7*3, 1)
   z = Oscar.RepPc.reps(abelian_closure(QQ)[1], G)
diff --git a/src/Groups/homomorphisms.jl b/src/Groups/homomorphisms.jl
index c790e9546911..6f81429d2b22 100644
--- a/src/Groups/homomorphisms.jl
+++ b/src/Groups/homomorphisms.jl
@@ -534,8 +534,16 @@ function isomorphism(::Type{FPGroup}, G::GAPGroup; on_gens::Bool=false)
    isos = get_attribute!(Dict{Tuple{Type, Bool}, Any}, G, :isomorphisms)::Dict{Tuple{Type, Bool}, Any}
    return get!(isos, (FPGroup, on_gens)) do
      if on_gens
-       f = GAPWrap.IsomorphismFpGroupByGenerators(G.X,
-             GAP.Globals.GeneratorsOfGroup(G.X))
+       Ggens = GAPWrap.GeneratorsOfGroup(G.X)
+       if length(Ggens) == 0
+# TODO: remove this special treatment as soon as the change from
+#       https://github.com/gap-system/gap/pull/5700 is available in Oscar
+#       (not yet in GAP 4.13.0)
+         f = GAP.Globals.GroupHomomorphismByImages(G.X, GAP.Globals.FreeGroup(0), GAP.Obj([]), GAP.Obj([]))
+         GAP.Globals.SetIsBijective(f, true)
+       else
+         f = GAPWrap.IsomorphismFpGroupByGenerators(G.X, Ggens)
+       end
      else
        f = GAPWrap.IsomorphismFpGroup(G.X)
      end
diff --git a/test/Groups/homomorphisms.jl b/test/Groups/homomorphisms.jl
index 74f7420501fd..a8963636ab53 100644
--- a/test/Groups/homomorphisms.jl
+++ b/test/Groups/homomorphisms.jl
@@ -425,6 +425,8 @@ end
        @test [preimage(f2, x) for x in gens(codomain(f2))] == gens(G)
        @test [preimage(f, x) for x in gens(codomain(f))] != gens(G)
 
+       @test is_bijective(isomorphism(FPGroup, symmetric_group(1), on_gens = true))
+
        G = abelian_group(PermGroup, [2, 2])
        f = @inferred isomorphism(FinGenAbGroup, G)
        @test codomain(f) isa FinGenAbGroup