diff --git a/src/Groups/GAPGroups.jl b/src/Groups/GAPGroups.jl
index 60936f65ee4e..b7a27376d621 100644
--- a/src/Groups/GAPGroups.jl
+++ b/src/Groups/GAPGroups.jl
@@ -367,16 +367,10 @@ comm(x::GAPGroupElem, y::GAPGroupElem) = x^-1*x^y
 Base.IteratorSize(::Type{<:GAPGroup}) = Base.SizeUnknown()
 Base.IteratorSize(::Type{PermGroup}) = Base.HasLength()
 
-function Base.iterate(G::GAPGroup)
-  L = GAPWrap.Iterator(G.X)::GapObj
-  i = GAPWrap.NextIterator(L)::GapObj
-  return group_element(G, i), L
-end
+Base.iterate(G::GAPGroup) = iterate(G, GAPWrap.Iterator(G.X))
 
 function Base.iterate(G::GAPGroup, state)
-  if GAPWrap.IsDoneIterator(state)
-    return nothing
-  end
+  GAPWrap.IsDoneIterator(state) && return nothing
   i = GAPWrap.NextIterator(state)::GapObj
   return group_element(G, i), state
 end
@@ -680,9 +674,7 @@ Base.IteratorSize(::Type{<:GAPGroupConjClass}) = Base.SizeUnknown()
 Base.iterate(cc::GAPGroupConjClass) = iterate(cc, GAPWrap.Iterator(cc.CC))
 
 function Base.iterate(cc::GAPGroupConjClass{S,T}, state::GapObj) where {S,T}
-  if GAPWrap.IsDoneIterator(state)
-    return nothing
-  end
+  GAPWrap.IsDoneIterator(state) && return nothing
   i = GAPWrap.NextIterator(state)::GapObj
   if T <: GAPGroupElem
      return group_element(cc.X, i), state
diff --git a/src/Groups/cosets.jl b/src/Groups/cosets.jl
index 90f6bb5f1fe6..bee4731cfc9f 100644
--- a/src/Groups/cosets.jl
+++ b/src/Groups/cosets.jl
@@ -436,9 +436,7 @@ Base.IteratorSize(::Type{<:GroupCoset}) = Base.SizeUnknown()
 Base.iterate(G::GroupCoset) = iterate(G, GAPWrap.Iterator(G.X))
 
 function Base.iterate(G::GroupCoset, state)
-  if GAPWrap.IsDoneIterator(state)
-    return nothing
-  end
+  GAPWrap.IsDoneIterator(state) && return nothing
   i = GAPWrap.NextIterator(state)::GapObj
   return group_element(G.G, i), state
 end
@@ -614,9 +612,7 @@ Base.IteratorSize(::Type{<:GroupDoubleCoset}) = Base.SizeUnknown()
 Base.iterate(G::GroupDoubleCoset) = iterate(G, GAPWrap.Iterator(G.X))
 
 function Base.iterate(G::GroupDoubleCoset, state)
-  if GAPWrap.IsDoneIterator(state)
-    return nothing
-  end
+  GAPWrap.IsDoneIterator(state) && return nothing
   i = GAPWrap.NextIterator(state)::GapObj
   return group_element(G.G, i), state
 end
diff --git a/src/Groups/matrices/MatGrp.jl b/src/Groups/matrices/MatGrp.jl
index 538dcacf0af2..e6348c1f1ae0 100644
--- a/src/Groups/matrices/MatGrp.jl
+++ b/src/Groups/matrices/MatGrp.jl
@@ -242,17 +242,10 @@ end
 
 Base.IteratorSize(::Type{<:MatrixGroup}) = Base.SizeUnknown()
 
-function Base.iterate(G::MatrixGroup)
-  L=GAPWrap.Iterator(G.X)::GapObj
-  @assert ! GAPWrap.IsDoneIterator(L)
-  i = GAPWrap.NextIterator(L)::GapObj
-  return MatrixGroupElem(G, i), L
-end
+Base.iterate(G::MatrixGroup) = iterate(G, GAPWrap.Iterator(G.X))
 
 function Base.iterate(G::MatrixGroup, state::GapObj)
-  if GAPWrap.IsDoneIterator(state)
-    return nothing
-  end
+  GAPWrap.IsDoneIterator(state) && return nothing
   i = GAPWrap.NextIterator(state)::GapObj
   return MatrixGroupElem(G, i), state
 end