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Article
Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities
Journal of Group Theory
  • Benjamin Fine, Fairfield University
  • Anthony M. Gaglione
  • A. G. Myasnikov
  • Dennis Spellman
Document Type
Article
Article Version
Publisher's PDF
Publication Date
1-1-2002
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

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
None
Peer Reviewed
Citation Information
Benjamin Fine, Anthony M. Gaglione, A. G. Myasnikov and Dennis Spellman. "Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities" Journal of Group Theory Vol. 5 Iss. 3 (2002)
Available at: http://works.bepress.com/benjamin_fine/3/