diff --git a/gap/attributes/attr.gd b/gap/attributes/attr.gd
index 06a89023a..8ab77e43d 100644
--- a/gap/attributes/attr.gd
+++ b/gap/attributes/attr.gd
@@ -53,7 +53,6 @@ DeclareAttribute("SmallestElementSemigroup", IsSemigroup);
 DeclareAttribute("LargestElementSemigroup", IsSemigroup);
 
 DeclareAttribute("StructureDescription", IsBrandtSemigroup);
-DeclareAttribute("StructureDescription", IsGroupAsSemigroup);
 DeclareAttribute("StructureDescriptionMaximalSubgroups",
                  IsSemigroup);
 DeclareAttribute("MaximalDClasses", IsSemigroup);
diff --git a/gap/attributes/attr.gi b/gap/attributes/attr.gi
index 096abd016..363c1299a 100644
--- a/gap/attributes/attr.gi
+++ b/gap/attributes/attr.gi
@@ -396,7 +396,7 @@ end);
 
 # same method for ideals
 
-InstallMethod(StructureDescription, "for a group as semigroup",
+InstallOtherMethod(StructureDescription, "for a group as semigroup",
 [IsGroupAsSemigroup],
 function(S)
   if IsGroup(S) then
diff --git a/gap/attributes/factor.gd b/gap/attributes/factor.gd
index 91add8019..c609d2698 100644
--- a/gap/attributes/factor.gd
+++ b/gap/attributes/factor.gd
@@ -13,5 +13,9 @@ DeclareOperation("MinimalFactorization",
 DeclareOperation("NonTrivialFactorization",
                  [IsSemigroup, IsMultiplicativeElement]);
 DeclareOperation("Factorization", [IsLambdaOrb, IsPosInt, IsPerm]);
-DeclareOperation("Factorization", [IsSemigroup, IsMultiplicativeElement]);
+DeclareOperation("Factorization",
+                 [IsSemigroup and CanUseFroidurePin, IsMultiplicativeElement]);
+DeclareOperation("Factorization",
+                 [IsActingSemigroup and HasGeneratorsOfSemigroup,
+                  IsMultiplicativeElement]);
 DeclareOperation("TraceSchreierTreeForward", [IsSemigroupData, IsPosInt]);
diff --git a/gap/semigroups/semifp.gd b/gap/semigroups/semifp.gd
index bcf6c3fef..acba8be2a 100644
--- a/gap/semigroups/semifp.gd
+++ b/gap/semigroups/semifp.gd
@@ -26,3 +26,8 @@ DeclareOperation("ReversedOp", [IsElementOfFpMonoid]);
 
 DeclareGlobalFunction("FreeMonoidAndAssignGeneratorVars");
 DeclareGlobalFunction("FreeSemigroupAndAssignGeneratorVars");
+
+DeclareOperation("Factorization", [IsFpSemigroup, IsElementOfFpSemigroup]);
+DeclareOperation("Factorization", [IsFpMonoid, IsElementOfFpMonoid]);
+DeclareOperation("Factorization", [IsFreeSemigroup, IsWord]);
+DeclareOperation("Factorization", [IsFreeMonoid, IsWord]);
diff --git a/gap/semigroups/semitrans.gd b/gap/semigroups/semitrans.gd
index ee12c8502..675cf48e4 100644
--- a/gap/semigroups/semitrans.gd
+++ b/gap/semigroups/semitrans.gd
@@ -42,8 +42,11 @@ DeclareOperation("EndomorphismMonoid", [IsDigraph, IsHomogeneousList]);
 DeclareAttribute("DigraphCore", IsDigraph);
 
 DeclareOperation("WreathProduct",
-                 [IsMultiplicativeElementCollection,
-                  IsMultiplicativeElementCollection]);
+                 [IsTransformationMonoid, IsPermGroup]);
+DeclareOperation("WreathProduct",
+                 [IsPermGroup, IsTransformationSemigroup]);
+DeclareOperation("WreathProduct",
+                 [IsTransformationMonoid, IsTransformationSemigroup]);
 
 DeclareAttribute("SmallestElementRClass", IsGreensRClass);
 DeclareAttribute("LargestElementRClass", IsGreensRClass);