LEVI CLASSES OF QUASIVARIETIES OF NILPOTENT GROUPS OF EXPONENT ps

被引：3
作者：
Lodeishchikova, V. V. [1 ]
Shakhova, S. A. [2 ]
机构：
[1] Altai State Tech Univ, Barnaul, Russia
[2] Altai State Univ, Barnaul, Russia
来源：
ALGEBRA AND LOGIC | 2022年 / 61卷 / 01期
关键词：
quasivariety; Levi class; nilpotent group;
D O I：
10.1007/s10469-022-09674-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Levi class L(M) generated by the class M of groups is the class of all groups in which the normal closure of every element belongs to M. It is proved that there exists a set of quasivarieties M of cardinality continuum such that L(M) = L(qH(ps)), where qH(ps) is the quasivariety generated by the group H-ps a free group of rank 2 in the variety R-Ps of <= 2-step nilpotent groups of exponent p(s) with commutator subgroup of exponent p, p is a prime number, p not equal 2, s is a natural number, s >= 2, and s > 2 for p = 3.
引用
收藏
页码：54 / 66
页数：13
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