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Archiv der Mathematik

, Volume 83, Issue 2, pp 106–112 | Cite as

The axiomatic closure of the class of discriminating groups

  • B. Fine
  • A. M. Gaglione
  • D. Spellman
Original paper

Abstract.

In [6] squarelike groups were defined to be those groups G universally equivalent to their direct squares G × G. In that paper it was shown that G is squarelike if and only if G is universally equivalent to a discriminating group in the sense of [3]. Further it was shown that the class of squarelike groups is first-order axiomatizable while the class of discriminating groups is not. In this paper, we prove that the class of squarelike groups is the least axiomatic class containing the discriminating groups.

Mathematics Subject Classification (2000):

Primary 20A05 Secondary 08C10 20E26. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsFairfield UniversityFairfieldUSA
  2. 2.Department of MathematicsU.S. Naval AcademyAnnapolisUSA
  3. 3.Department of MathematicsTemple UniversityPhiladelphiaUSA

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