Products of Conjugacy Classes in a Free Group: a Counterexample.
For the groups , , , over a finite field we solve the class product problem, i.e., we give a complete list of -tuples of conjugacy classes whose product does not contain the identity matrix.
We describe necessary and sufficient conditions for a direct product and a lexicographic product of partially ordered quasigroups to be a positive quasigroup. Analogous questions for Riesz quasigroups are studied.