gh-101277: Isolate itertools, add group and _grouper types to module state (#101302)

Co-authored-by: Kumar Aditya <59607654+kumaraditya303@users.noreply.github.com>

Lib/test/test_itertools.py

@@ -1694,6 +1694,38 @@ class TestBasicOps(unittest.TestCase):
         gc.collect()
         self.assertTrue(gc.is_tracked(next(it)))
 
+    @support.cpython_only
+    def test_immutable_types(self):
+        from itertools import _grouper, _tee, _tee_dataobject
+        dataset = (
+            accumulate,
+            batched,
+            chain,
+            combinations,
+            combinations_with_replacement,
+            compress,
+            count,
+            cycle,
+            dropwhile,
+            filterfalse,
+            groupby,
+            _grouper,
+            islice,
+            pairwise,
+            permutations,
+            product,
+            repeat,
+            starmap,
+            takewhile,
+            _tee,
+            _tee_dataobject,
+            zip_longest,
+        )
+        for tp in dataset:
+            with self.subTest(tp=tp):
+                with self.assertRaisesRegex(TypeError, "immutable"):
+                    tp.foobar = 1
+
 
 class TestExamples(unittest.TestCase):