Fix cached orbits inside orbits (#4753)

Author: lgoettgens

src/Groups/gsets.jl

@@ -376,7 +376,7 @@ function _orbit_generic(Omega::GSetByElements{<:GAPGroup, S}, omega::S) where S
 
     res = as_gset(acting_group(Omega), action_function(Omega), orb)
     # We know that this G-set is transitive.
-    set_attribute!(res, :orbits => [orb])
+    set_attribute!(res, :orbits => [res])
     return res
 end
 #T check whether omega lies in Omega?
@@ -409,7 +409,7 @@ function _orbit_special_GAP(Omega::GSetByElements{<:GAPGroup, S}, omega::S) wher
 
     res = as_gset(acting_group(Omega), action_function(Omega), orb)
     # We know that this G-set is transitive.
-    set_attribute!(res, :orbits => [orb])
+    set_attribute!(res, :orbits => [res])
     return res
 end
 
@@ -435,7 +435,7 @@ function orbit_via_Julia(Omega::GSet, omega)
 
     res = as_gset(acting_group(Omega), action_function(Omega), orbarray)
     # We know that this G-set is transitive.
-    set_attribute!(res, :orbits => [orbarray])
+    set_attribute!(res, :orbits => [res])
     return res
 end
 

test/Groups/gsets.jl

@@ -153,7 +153,9 @@
   # orbit
   G = symmetric_group(6)
   Omega = gset(G, permuted, [[0,1,0,1,0,1], [1,2,3,4,5,6]])
-  @test length(orbit(Omega, [0,1,0,1,0,1])) == length(Oscar.orbit_via_Julia(Omega, [0,1,0,1,0,1]))
+  orb = orbit(Omega, [0,1,0,1,0,1])
+  @test length(orb) == length(Oscar.orbit_via_Julia(Omega, [0,1,0,1,0,1]))
+  @test orbits(orb) == [orb]
 
   # permutation
   G = symmetric_group(6)