Geometric equivalence of $\pi$-torsion free nilpotent groups

Lipyanski Ruvim

Geometric equivalence of $\pi$-torsion free nilpotent groups

Algebraic Geometry 2018-02-06 v1 Group Theory

Authors: Lipyanski Ruvim

Abstract

In this paper we study the property of geometric equivalence of groups introduced by B. Plotkin \cite{P1, P2}. Sufficient and necessary conditions are presented for a $\pi$ -torsion-free nilpotent group to be geometrically equivalent to its $\pi$ -completion. We prove that a relatively free nilpotent $\pi$ -torsion-free group and its $\pi$ -completion define the same quasi-variety. Examples of $\pi$ -torsion-free nilpotent groups that are geometrically equivalent to their $\pi$ -completions are given.

Keywords

geometric equivalence π-torsion-free nilpotent groups π-completion quasi-variety relatively free groups

Cite

@article{arxiv.1802.01098,
  title  = {Geometric equivalence of $\pi$-torsion free nilpotent groups},
  author = {Lipyanski Ruvim},
  journal= {arXiv preprint arXiv:1802.01098},
  year   = {2018}
}

Comments

11 pages

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