Title

Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities

Authors

Benjamin Fine, Fairfield UniversityFollow
Anthony M. Gaglione
A. G. Myasnikov
Dennis Spellman

Document Type

Article

Article Version

Publisher's PDF

Publication Date

2002

Abstract

Discriminating groups were introduced in [3] with an eye toward applications to the universal theory of various groups. In [6] it was shown that if G is any discriminating group, then the universal theory of G coincides with that of its direct square G x G. In this paper we explore groups G whose universal theory coincides with that of their direct square. These are called square-like groups. We show that the class of square-like groups is first-order axiomatizable and contains the class of discriminating groups as a proper subclass. Further we show that the class of discriminating groups is not first-order axiomatizable.

Comments

Original published version can be found at DOI: 10.1515/jgth.2002.009

Publication Title

Journal of Group Theory

Repository Citation

Fine, Benjamin; Gaglione, Anthony M.; Myasnikov, A. G.; and Spellman, Dennis, "Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities" (2002). Mathematics Faculty Publications. 6.
https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/6

Published Citation

B. Fine, A. M. Gaglione, A. G. Myasnikov, and D. Spellman. Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities, Journal of Group Theory. 5(3), 365-381.

DOI

10.1515/jgth.2002.009

Peer Reviewed