Semigroup laws in varieties of solvable groups
Jacques Lewin, Tekla Lewin · Mathematical Proceedings of the Cambridge Philosophical Society · 1969
Let be a variety of groups. We say that the variety (the group G) has a semigroup law if u(x1, …, xn) = ν(x1, …, xn) is a law in (in G), with u and ν different words in the free semigroup freely generated by x1,…,xn. It seems very difficult to determine under what conditions a variety has a semigroup law. All we can say in general is that if does have a semigroup law, then it is in fact characterized by its semigroup laws (Section III).