Groups whose universal theory is axiomatizable by quasi-identities

Benjamin Fine, Anthony M. Gaglione, Alexei Myasnikov, Dennis Spellman

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 × 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.

Original languageEnglish
Pages (from-to)365-381
Number of pages17
JournalJournal of Group Theory
Volume5
Issue number3
DOIs
StatePublished - 2002

Fingerprint

Dive into the research topics of 'Groups whose universal theory is axiomatizable by quasi-identities'. Together they form a unique fingerprint.

Cite this