Presentation of A Group - Deficiency

The deficiency of a finite presentation <S|R> is just |S| - |R| and the deficiency of a finitely presented group G, denoted def G, is the maximum of the deficiency over all presentations of G. The deficiency of a finite group is non-positive. The Schur multiplicator of a group G can be generated by −def G generators, and G is efficient if this number is required.

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