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In [53]: a = pd.DataFrame({'a': [1, 1, 2], 'b': [1, 2, 3], 'c': [1, 2, 4]})
In [54]: a.groupby('a').agg({'c': ['min']}) # name preserved in index
Out[54]:
c
min
a
1 1
2 4
In [55]: a.groupby('a').agg({'b': [], 'c': ['min']}) # name lost in index
Out[55]:
c
min
1 1
2 4
In the above snippet, the name of the grouped by column ('a') is preserved in the former case, and lost in the latter case.