Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities

Benjamin Fine; Anthony M. Gaglione; A. G. Myasnikov; Dennis Spellman

doi:10.1515/jgth.2002.009

Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities

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

Fairfield University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Journal of Group Theory
Volume	5
DOIs	https://doi.org/10.1515/jgth.2002.009
State	Published - Jan 1 2002

Disciplines

Computer Sciences
Physical Sciences and Mathematics

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title = "Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities",

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.",

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AB - 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.

UR - https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/6

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JO - Journal of Group Theory

JF - Journal of Group Theory

ER -

Groups Whose Universal Theory Is Axiomatizable by Quasi-Identities

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