We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.
"A Computer Algebra Solution to a Problem in Finite Groups." Rev. Mat. Iberoamericana 19 (2) 413 - 424, September, 2003.