This article is cited in 2 papers

On quasivarieties of axiomatic rank $3$ of torsion-free nilpotent groups

A. I. Budkin

Altai State University, Barnaul, Russia

Abstract: We study the lattice of quasivarieties of axiomatic rank at most $3$ of torsion-free nilpotent groups of class at most $3$. We prove that this lattice has cardinality of the continuum and includes a sublattice that is order isomorphic to the set of real numbers. Also we establish that the lattice of quasivarieties of axiomatic rank at most $2$ of these groups is a $5$-element chain.

Keywords: nilpotent group, axiomatic rank, quasivarieties, lattice.

UDC: 512.57

Received: 02.03.2016

DOI: 10.17377/smzh.2017.58.106

 English version: Siberian Mathematical Journal, 2017, 58:1, 43–48

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