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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-7,
author = {B. Bajorska and O. Macedo\'nska},
title = {On the Boffa alternative},
journal = {Colloquium Mathematicae},
volume = {89},
year = {2001},
pages = {257-261},
zbl = {0986.20031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-7}
}
B. Bajorska; O. Macedońska. On the Boffa alternative. Colloquium Mathematicae, Tome 89 (2001) pp. 257-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm88-2-7/