TST: Add test inconsistency in group by (#44803) (#45509)

Author: NumberPiOso

pandas/tests/groupby/test_groupby.py

@@ -32,6 +32,20 @@
 from pandas.core.groupby.base import maybe_normalize_deprecated_kernels
 
 
+def test_group_by_copy():
+    # GH#44803
+    df = DataFrame(
+        {
+            "name": ["Alice", "Bob", "Carl"],
+            "age": [20, 21, 20],
+        }
+    ).set_index("name")
+
+    grp_by_same_value = df.groupby(["age"]).apply(lambda group: group)
+    grp_by_copy = df.groupby(["age"]).apply(lambda group: group.copy())
+    tm.assert_frame_equal(grp_by_same_value, grp_by_copy)
+
+
 def test_repr():
     # GH18203
     result = repr(Grouper(key="A", level="B"))