Pandas Group keys are not added to DataFrame's groupby result

Code Sample, a copy-pastable example if possible

df = pd.DataFrame({'x':[1,2,3,4,5,6], 'y':[6,5,7,4,3,5], 'z':list('qqqrrs')})

def f(df):
    return df.sort_values(by='x')

def g(df):    
    return df

print(df.groupby('z', group_keys=True).apply(f)) # Group keys are added
print(df.groupby('z', group_keys=True).apply(g)) # Group keys are not added

Problem description

Because df is already sorted for all columns, the groupby result should be same. However they are different: only for the case of df.sort_result() correctly adds group keys to the groupby result.

PS: I have one observation. if g(df) returned df[::] instead of df, then groupkeys were added.

Expected Output

Since group_keys=True, the output should look like the following:

     x  y  z
z           
q 0  1  6  q
  1  2  5  q
  2  3  7  q
r 3  4  4  r
  4  5  3  r
s 5  6  5  s

Output of `pd.show_versions()`

[paste the output of ``pd.show_versions()`` here below this line] INSTALLED VERSIONS ------------------ commit: None python: 3.6.3.final.0 python-bits: 64 OS: Windows OS-release: 10 machine: AMD64 processor: Intel64 Family 6 Model 94 Stepping 3, GenuineIntel byteorder: little LC_ALL: None LANG: None LOCALE: None.None pandas: 0.20.3 pytest: 3.2.1 pip: 10.0.1 setuptools: 36.5.0.post20170921 Cython: 0.26.1 numpy: 1.14.0 scipy: 0.19.1 xarray: None IPython: 6.1.0 sphinx: 1.6.3 patsy: 0.4.1 dateutil: 2.6.1 pytz: 2017.2 blosc: None bottleneck: 1.2.1 tables: 3.4.2 numexpr: 2.6.2 feather: None matplotlib: 2.1.0 openpyxl: 2.4.8 xlrd: 1.1.0 xlwt: 1.3.0 xlsxwriter: 1.0.2 lxml: 4.1.0 bs4: 4.6.0 html5lib: 0.999999999 sqlalchemy: 1.1.13 pymysql: None psycopg2: None jinja2: 2.10 s3fs: None pandas_gbq: None pandas_datareader: 0.7.0

Pandas Group keys are not added to DataFrame's groupby result

Code Sample, a copy-pastable example if possible

Problem description

Expected Output

Output of pd.show_versions()

Output of `pd.show_versions()`