On the Boffa alternative
Volume 88 / 2001
Colloquium Mathematicum 88 (2001), 257-261
MSC: 20F19, 20E10.
DOI: 10.4064/cm88-2-7
Abstract
Let $G^*$ denote a nonprincipal ultrapower of a group $G$. In 1986 M.~Boffa posed a question equivalent to the following one: if $G$ does not satisfy a positive law, does $G^*$ contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.
