Geometric equivalence of π-torsion free nilpotent groups

2018/02/04 by Lipyanski Ruvim, Ruvim, Lipyanski
Mathematics · #14A20 #20D15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Primary 20F18 #Secondary 14A22 #math.AG #math.GR #msc:14A20 #msc:14A22 #msc:20D15 #msc:20F18

paper · pdf · doi:10.48550/arxiv.1802.01098

11 pages

arxiv created 2018/02/04 · arxiv updated 2018/02/06

Abstract

In this paper we study the property of geometric equivalence of groups introduced by B. Plotkin \citeP1, P2. Sufficient and necessary conditions are presented for a π-torsion-free nilpotent group to be geometrically equivalent to its π-completion. We prove that a relatively free nilpotent π-torsion-free group and its π-completion define the same quasi-variety. Examples of π-torsion-free nilpotent groups that are geometrically equivalent to their π-completions are given.

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