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To the best of my knowledge, .groups() returns a tuple of remembered groups. I.e. those groups in the regular expression that are enclosed in parentheses. So if you were to write:
print re.search(r'(1)', '1').groups()
you would get
('1',)
as your response. In general, .groups() will return a tuple of all the groups of objects in the regular expression that are enclosed within parentheses.
groups is empty since you do not have any capturing groups - http://docs.python.org/library/re.html#re.MatchObject.groups. group(0) will always returns the whole text that was matched regardless of if it was captured in a group or not
Edited.