You need filtration :
df = df.groupby('letter').filter(lambda x: (x['number'] == 0).any())
print (df)
letter number
0 a 2
1 a 0
5 c 1
6 c 0
7 c 2
Another solution with transformwhere to get the 0row size and filter boolean indexing:
print (df.groupby('letter')['number'].transform(lambda x: (x == 0).sum()))
0 1
1 1
2 0
3 0
4 0
5 1
6 1
7 1
Name: number, dtype: int64
df = df[df.groupby('letter')['number'].transform(lambda x: (x == 0).sum()) > 0]
print (df)
letter number
0 a 2
1 a 0
5 c 1
6 c 0
7 c 2
EDIT:
Faster is not used groupby, better locwith : isin
df1 = df[df['letter'].isin(df.loc[df['number'] == 0, 'letter'])]
print (df1)
letter number
0 a 2
1 a 0
5 c 1
6 c 0
7 c 2
Comparison with another solution:
In [412]: %timeit df[df['letter'].isin(df[df['number'] == 0]['letter'])]
1000 loops, best of 3: 815 µs per loop
In [413]: %timeit df[df['letter'].isin(df.loc[df['number'] == 0, 'letter'])]
1000 loops, best of 3: 657 µs per loop
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