In [1]: import pandas as pd
   ...:
   ...: data = {'m': ['m1','m2','m2','m3','m3','m3','m4','m4','m4','m4'],
   ...:         'e': ['e1','e2','e3','e4','e5','e6','e7','e1','e2','e8'],
   ...:         'p': [0.9, 0.2, 0.8, 0.7, 0.1, 0.2, 0.3, 0.1, 0.2, 0.4]}
   ...: df = pd.DataFrame(data)
   ...: df
   ...:
Out[1]:
    e   m    p
0  e1  m1  0.9
1  e2  m2  0.2
2  e3  m2  0.8
3  e4  m3  0.7
4  e5  m3  0.1
5  e6  m3  0.2
6  e7  m4  0.3
7  e1  m4  0.1
8  e2  m4  0.2
9  e8  m4  0.4

In [2]: gm = df.groupby(by=['m'])

In [3]: count = gm['e'].count()
   ...: count = count.to_frame()
   ...: count.columns = ['count']
   ...: count
   ...:
Out[3]:
    count
m
m1      1
m2      2
m3      3
m4      4

In [4]: maxp = gm['p'].max()
   ...: maxp = maxp.to_frame()
   ...: maxp.columns = ['maxp']
   ...: maxp
   ...:
Out[4]:
    maxp
m
m1   0.9
m2   0.8
m3   0.7
m4   0.4

In [5]: df = pd.merge(df, count, left_on='m', right_index=True)
   ...: df = pd.merge(df, maxp, left_on='m', right_index=True)
   ...: df
   ...:
Out[5]:
    e   m    p  count  maxp
0  e1  m1  0.9      1   0.9
1  e2  m2  0.2      2   0.8
2  e3  m2  0.8      2   0.8
3  e4  m3  0.7      3   0.7
4  e5  m3  0.1      3   0.7
5  e6  m3  0.2      3   0.7
6  e7  m4  0.3      4   0.4
7  e1  m4  0.1      4   0.4
8  e2  m4  0.2      4   0.4
9  e8  m4  0.4      4   0.4