Geodesic
Varieties in which all finite groups are Abelian
Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 57-80

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The well-known problem of the existence of a variety that contains non-Abelian groups, but in which all finite groups are Abelian, is solved affirmatively. The variety $\mathfrak M$ is given by a single two-variable identity. For the proof, the author inductively introduces defining relations for $\mathfrak M$-free groups. In the study of their consequences, he uses a geometrical interpretation for deduction. The exposition is heavily dependent on a previous paper of the author. Figures: 4. Bibliography: 7 titles. 
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     author = {A. Yu. Ol'shanskii},
     title = {Varieties in which all finite groups are {Abelian}},
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A. Yu. Ol'shanskii. Varieties in which all finite groups are Abelian. Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 57-80. http://geodesic.mathdoc.fr/item/SM_1986_54_1_a2/