Anthony M. Gaglione ; Dennis Spellman - An axiomatization for the universal theory of the Heisenberg group

gcc:12200 - journal of Groups, complexity, cryptology, August 31, 2023, Volume 15, Issue 1 - https://doi.org/10.46298/jgcc.2023..12200
An axiomatization for the universal theory of the Heisenberg groupArticle

Authors: 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.


    Volume: Volume 15, Issue 1
    Published on: August 31, 2023
    Accepted on: August 29, 2023
    Submitted on: August 29, 2023
    Keywords: Mathematics - Group Theory,Mathematics - Logic,Primary 05C38, 15A15, Secondary 05A15, 15A18

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