An axiomatization for the universal theory of the Heisenberg groupArticle
Authors: Anthony M. Gaglione ; Dennis Spellman
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Anthony M. Gaglione;Dennis Spellman
The Heisenberg group, here denoted $H$, is the group of all $3\times 3$ upper
unitriangular matrices with entries in the ring $\mathbb{Z}$ of integers. A.G.
Myasnikov posed the question of whether or not the universal theory of $H$, in
the language of $H$, is axiomatized, when the models are restricted to
$H$-groups, by the quasi-identities true in $H$ together with the assertion
that the centralizers of noncentral elements be abelian. Based on earlier
published partial results we here give a complete proof of a slightly stronger
result.