On the Boffa alternative
Tom 88 / 2001
Colloquium Mathematicum 88 (2001), 257-261
MSC: 20F19, 20E10.
DOI: 10.4064/cm88-2-7
Streszczenie
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.
