Varieties in which all finite groups are Abelian

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.