You need the first captured group:

a.group(1)
b.group(1)
...

without any captured group specification as argument to group(), it will show the full match, like what you're getting now.

Here's an example:

In [8]: string_one = 'file_record_transcript.pdf'

In [9]: re.search(r'^(file.*)\.pdf$', string_one).group()
Out[9]: 'file_record_transcript.pdf'

In [10]: re.search(r'^(file.*)\.pdf$', string_one).group(1)
Out[10]: 'file_record_transcript'

You could create a little class that returns the boolean result of calling match, and retains the matched groups for subsequent retrieval:

import re

class REMatcher(object):
    def __init__(self, matchstring):
        self.matchstring = matchstring

    def match(self,regexp):
        self.rematch = re.match(regexp, self.matchstring)
        return bool(self.rematch)

    def group(self,i):
        return self.rematch.group(i)


for statement in ("I love Mary", 
                  "Ich liebe Margot", 
                  "Je t'aime Marie", 
                  "Te amo Maria"):

    m = REMatcher(statement)

    if m.match(r"I love (\w+)"): 
        print "He loves",m.group(1) 

    elif m.match(r"Ich liebe (\w+)"):
        print "Er liebt",m.group(1) 

    elif m.match(r"Je t'aime (\w+)"):
        print "Il aime",m.group(1) 

    else: 
        print "???"

Update for Python 3 print as a function, and Python 3.8 assignment expressions - no need for a REMatcher class now:

import re

for statement in ("I love Mary",
                  "Ich liebe Margot",
                  "Je t'aime Marie",
                  "Te amo Maria"):

    if m := re.match(r"I love (\w+)", statement):
        print("He loves", m.group(1))

    elif m := re.match(r"Ich liebe (\w+)", statement):
        print("Er liebt", m.group(1))

    elif m := re.match(r"Je t'aime (\w+)", statement):
        print("Il aime", m.group(1))

    else:
        print()

For re details consult docs. In your case:

group(0) stands for all matched string, hence abc, that is 3 groups a, b and c

group(i) stands for i'th group, and citing documentation

If a group matches multiple times, only the last match is accessible

hence group(1) stands for last match, c

Your + is interpreted as group repetation, if you want repeat [abc] inside group, move + into parentheses:

Copy>>> re.match("([abc])", "abc").groups()
('a',)
>>> re.match("([abc]+)", "abc").groups()
('abc',)