Add yes if within a group, a column contains all element from a list in python

I have a dataframe such as :

The_list=["A","B"]

Groups COL2
G1     A
G1     B
G1     C
G2     A
G2     D
G3     A
G3     B
G4     A
G5     B

and I would like to add another COL3 column where I put yes for each Groups where all element from The_list are present within the COL2, and no if not.

I should then get :

Groups COL2 COL3
G1     A    yes
G1     B    yes
G1     C    yes
G2     A    no
G2     D    no
G3     A    yes
G3     B    yes
G4     A    no
G5     B    no

>Solution :

Use Groupby.apply with set intersection and np.where:

# Group on column 'Groups' and apply set intersection and find length of set
In [1178]: out = df.groupby('Groups')['COL2'].apply(lambda x: len(set(x) & set(The_list))).reset_index()

# If length of set is equal to the length of the list, then 'yes' else 'no'
In [1179]: import numpy as np
In [1180]: out['COL3'] = np.where(out.COL2.eq(len(The_list), 'yes', 'no')

# Merge original df with above and populate COL3
In [1185]: df = df.merge(out[['Groups','COL3']])

In [1186]: df
Out[1186]: 
  Groups COL2 COL3
0     G1    A  yes
1     G1    B  yes
2     G1    C  yes
3     G2    A   no
4     G2    D   no
5     G3    A  yes
6     G3    B  yes
7     G4    A   no
8     G5    B   no