On Varieties of Groups Without Positive Laws

Abstract

We give negative answers to three questions concerning positive laws and A p A varieties.

On difficult problems and locally graded groups

“…The negative answer to the problem is given in [12]. It is shown that there exists a group G which contains a free non-abelian subsemigroup (hence it has no positive laws), while var(G) does not contain A p A for any p. This group G is the finitely generated relatively free group, which is studied in Chapter 9 of [20].…”