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A finite presentation F/N of a group G is called efficient if d F (N) = d(H 2 (G)) + d(F) -r(J/,(G)). A finitely presented group is called efficient if it admits an efficient presentation. We show that a finitely presented group embeds into an efficient group. 1991 Mathematics subject classification: 20F05.doi:10.1017/s0013091500023750 fatcat:dz746hcgpbazrdw25pehq24l3a