ON QUASIVARIETIES OF AXIOMATIC RANK 3 OF TORSION-FREE NILPOTENT GROUPS

被引：2
作者：
Budkin, A. I. [1 ]
机构：
[1] Altai State Univ, Barnaul, Russia
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2017年 / 58卷 / 01期
关键词：
nilpotent group; axiomatic rank; quasivarieties; lattice;
D O I：
10.1134/S0037446617010062
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：43 / 48
页数：6
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