Find rows where there are duplicates in another column in the designated group of another column

For the data set df, I want to groupby two groups of foo and bar in column B, and identify the duplicated rows that exist in both groups. How can I achieve this?

df = pd.DataFrame({'A': [1, 2, 2, 3, 3, 1],
                   'B': ['foo', 'bar', 'foo', 'bar', 'foo', 'foo']})
df = df.sort_values('B')
df
Out[15]: 
   A    B
1  2  bar
3  3  bar
0  1  foo
2  2  foo
4  3  foo
5  1  foo

The expected result:

   A    B  Indicator
1  2  bar  True  # value 2 also present in foo, so returns True
3  3  bar  True  # value 3 also present in foo, so returns True
0  1  foo  False  # value 1 only present in foo, so returns False
2  2  foo  True  # value 2 also present in bar, so returns True
4  3  foo  True  # value 3 also present in bar, so returns True
5  1  foo  False  # value 1 only present in foo, so returns False

Updates:

Assuming column B has more than 2 categories, the sample data df is as follows:

df = pd.DataFrame({'A': [1, 2, 2, 3, 3, 2, 1],  'B': ['foo', 'bar', 'foo', 'bar', 'foo', 'baz', 'baz']})
df = df.sort_values('B')
df
Out[30]: 
   A    B
1  2  bar
3  3  bar
5  2  baz
6  1  baz
0  1  foo
2  2  foo
4  3  foo

In this case, the expected result would be as follows:

   A    B  Indicator
1  2  bar  True  # The value 2 occurs in categories baz, bar, and foo, so returns True.
3  3  bar  False  # The value 3 only occurs in categories bar and foo, so returns False.
5  2  baz  True  # The value 2 occurs in categories baz, bar, and foo, so returns True.
6  1  baz  False  # The value 1 only occurs in categories baz and foo, so returns False.
0  1  foo  False  # The value 1 only occurs in categories baz and foo, so returns False.
2  2  foo  True  # The value 2 occurs in categories baz, bar, and foo, so returns True.
4  3  foo  False  # The value 3 only occurs in categories bar and foo, so returns False.

Since you have multiple groups, you can use:

data = {'A': [2, 3, 2, 1, 1, 2, 3],
        'B': ['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'foo']}
df = pd.DataFrame(data).sort_values('B')

df['Indicator'] = df.groupby('A')['B'].transform('nunique') == df['B'].nunique()

Output:

>>> df
   A    B  Indicator
0  2  bar       True
1  3  bar      False
2  2  baz       True
3  1  baz      False
4  1  foo      False
5  2  foo       True
6  3  foo      False

If need intersection B values per all A groups use:

First idea is use crosstab for get A values if exist in each group and filter A values in Series.isin:

df1 = pd.crosstab(df.A, df.B).astype(bool)

df['Indicator'] = df['A'].isin(df1.index[df1.all(axis=1)])
print(df)
   A    B  Indicator
1  2  bar       True
3  3  bar       True
0  1  foo      False
2  2  foo       True
4  3  foo       True
5  1  foo      False

Or use intersection of sets per groups by B for last DataFrame in question:

setlist = df.groupby('B')['A'].agg(set)
print (setlist)
B
bar       {2, 3}
baz       {1, 2}
foo    {1, 2, 3}
Name: A, dtype: object

u = set.intersection(*setlist)
print (u)
{2}

df['Indicator'] = df['A'].isin(u)
print (df)
   A    B  Indicator
1  2  bar       True
3  3  bar      False
5  2  baz       True
6  1  baz      False
0  1  foo      False
2  2  foo       True
4  3  foo      False
5  1  foo      False