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 Quote by Newtime Let G be a group given as a quotient f: F(S)--->G of the free group on the set S.
In this case the way to interpret it is that G is isomorphic to the quotient F(S)/ker f (assuming of course that f is surjective). Sometimes you won't be given the quotient directly, but you will instead be given an object from which you can construct the quotient.