Affine Geometry aspect of a joint work of T. Bandman, G.-M. Greuel, F. Grunewald,
B. Kunyavskii , G. Pfister, and Eu. Plotkin.
We characterize solvable groups within the class of finite groups by identities in two variables.
Although this is a purely group-theoretical result,
its proof involves surprisingly diverse methods of ring theory,
algebraic geometry, group theory, and computer algebra.