diff --git a/src/symbols.jl b/src/symbols.jl
index e13435c..a6258bc 100644
--- a/src/symbols.jl
+++ b/src/symbols.jl
@@ -1,7 +1,7 @@
 change_pow(s::S, n::Integer) where S<:GSymbol = S(s.id, n)
 
 function Base.iterate(s::GS, i=1) where GS<:GSymbol
-    return i <= abs(s.pow) ? (GS(s.id, sign(s.pow)), i+1) : nothing
+    return i <= abs(s.pow) ? (change_pow(s, sign(s.pow)), i+1) : nothing
 end
 Base.size(s::GSymbol) = (abs(s.pow), )
 Base.length(s::GSymbol) = first(size(s))
diff --git a/test/AutGroup-tests.jl b/test/AutGroup-tests.jl
index 0b9c658..234ac60 100644
--- a/test/AutGroup-tests.jl
+++ b/test/AutGroup-tests.jl
@@ -142,12 +142,17 @@
       @test (Groups.change_pow(f, -2)).pow == 1
       @test (inv(f)).pow == 1
 
-      f = Groups.AutSymbol(perm"(1,2)(3,4)")
-      @test isa(inv(f), Groups.AutSymbol)
+      g = Groups.AutSymbol(perm"(1,2)(3,4)")
+      @test isa(inv(g), Groups.AutSymbol)
 
-      @test_throws MethodError f*f
+      @test_throws MethodError g*f
 
-      @test A(f)^-1 == A(inv(f))
+      @test A(g)^-1 == A(inv(g))
+
+      h = Groups.transvection_R(1,2)
+
+      @test collect(A(g)*A(h)) == [g, h]
+      @test collect(A(h)^2) == [h, h]
    end
 
    @testset "reductions/arithmetic" begin