Sib. Èlektron. Mat. Izv., 2017, Volume 14, Pages 937–945
Mathematical logic, algebra and number theory
On groups which are not finitely defined in every quasivariety of groups
A. I. Budkin
Altai State University,
pr. Lenina, 61,
656049, Barnaul, Russia
We continue to study quasivarieties of groups closed under direct Z-wreath products. We show that such quasivarieties contain finitely generated groups which are not finitely defined in every quasivariety of groups.
We establish the existence of continuum many finitely generated groups every of which is not finitely defined in each quasivariety of groups.
We construct the group which is finitely defined in the class of all torsion-free groups and is not finitely defined in the class of all groups.
group, finitely defined group, quasivariety, wreath product.
PDF file (158 kB)
Received June 6, 2017, published September 15, 2017
A. I. Budkin, “On groups which are not finitely defined in every quasivariety of groups”, Sib. Èlektron. Mat. Izv., 14 (2017), 937–945
Citation in format AMSBIB
\paper On groups which are not finitely defined in every quasivariety of groups
\jour Sib. \`Elektron. Mat. Izv.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|