On the Boffa alternative

B. Bajorska, and O. Macedońska. "On the Boffa alternative." Colloquium Mathematicae 88.2 (2001): 257-261. <http://eudml.org/doc/284336>.

@article{B2001,
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.},
author = {B. Bajorska, O. Macedońska},
journal = {Colloquium Mathematicae},
keywords = {group laws; positive laws; free subsemigroups; ultrapowers of groups; products of varieties; varieties of groups; soluble groups; restricted Burnside varieties},
language = {eng},
number = {2},
pages = {257-261},
title = {On the Boffa alternative},
url = {http://eudml.org/doc/284336},
volume = {88},
year = {2001},
}

TY - JOUR
AU - B. Bajorska
AU - O. Macedońska
TI - On the Boffa alternative
JO - Colloquium Mathematicae
PY - 2001
VL - 88
IS - 2
SP - 257
EP - 261
AB - 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.
LA - eng
KW - group laws; positive laws; free subsemigroups; ultrapowers of groups; products of varieties; varieties of groups; soluble groups; restricted Burnside varieties
UR - http://eudml.org/doc/284336
ER -