[Python] Pandas - group by and filter

Here is my dataframe

my_df = pd.DataFrame({'col_1': ['A', 'A', 'B', 'B', 'C', 'C'],
'col_2': [1, 2, 1, 2, 1, 2]})


I would like to group by col_1 and filter out anything strictly greater than one using col_2. The final result should look like:

final_df = pd.DataFrame({'col_1': ['A', 'B', 'C'],
'col_2': [1, 1, 1, ]})


Here is what I tried:

df_ts = my_df.groupby('col_1').filter(lambda x: (x['col_2'] <= 1).any())


It returns the same dataframe

I also tried:

df_ts = my_df.groupby('col_1').filter(lambda x: x['col_2'] <= 1)


It generates error.

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