diff --git a/src/automorphism_groups.jl b/src/automorphism_groups.jl
index 51d2a48..6078840 100644
--- a/src/automorphism_groups.jl
+++ b/src/automorphism_groups.jl
@@ -100,5 +100,6 @@ function simplify_perms!(W::AutWord)
             end
         end
     end
+    deleteat!(W.symbols, find(x -> x.pow == 0, W.symbols))
     return reduced
 end