Added Doctests

Author: AdityaK1729

src/sage/groups/perm_gps/permgroup.py

@@ -3304,6 +3304,12 @@ def commutator(self, other=None):
             Traceback (most recent call last):
             ...
             TypeError: junk is not a permutation group
+        TESTS ::
+            
+        Verify that :issue`39416` is fixed::
+            sage: G = PermutationGroup(gens=[("a", "b"), ("b","c")])
+            sage: G.commutator()
+            Subgroup generated by [('a','b','c')] of (Permutation Group with generators [('b','c'), ('a','b')])
         """
         if other is None:
             return self.subgroup(gap_group=libgap.DerivedSubgroup(self))