TY - JOUR
T1 - Groups whose universal theory is axiomatizable by quasi-identities
AU - Fine, Benjamin
AU - Gaglione, Anthony M.
AU - Myasnikov, Alexei
AU - Spellman, Dennis
PY - 2002
Y1 - 2002
N2 - 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.
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 × 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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U2 - 10.1515/jgth.2002.009
DO - 10.1515/jgth.2002.009
M3 - Article
AN - SCOPUS:0036318692
SN - 1433-5883
VL - 5
SP - 365
EP - 381
JO - Journal of Group Theory
JF - Journal of Group Theory
IS - 3
ER -