An axiomatization for the universal theory of the Heisenberg group

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.Comment: 13 pages. Published in journal of Groups, Complexity, Cryptolog

The Persistence of Universal Formulae in Free Algebras

Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements ..

The Persistence of Universal Formulae in Free Algebras

Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements ..

Commutator Identities Obtained by the Magnus Algebra

In this paper, two related commutator identities are established through the use of the Magnus Algebra (the algebra of noncommutative formal power series with integral coefficients)

Environmental study of a Micromegas detector

We report on measurements of the basic performance of a Micromegas detector for a digital hadronic calorimeter. Electron collection efficiency, energy resolution and gas gain were measured in various mixtures of Ar and CO2. Also the dependence of the gain on environmental variables (pressure, temperature), gas parameters (flow, mixing ratio) and geometry (amplication gap size) is studied. Eventually, predictions on the impact of these variables on the detection efficiency of thin Micromegas detectors are drawn

Reflections on Discriminating Groups

Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [7]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R\u27 is non-discriminating