The lattice of quasivarieties of torsion-free metabelian groups

被引：0
作者：
A. I. Budkin
机构：
来源：
Algebra and Logic | 2003年 / 42卷 / 2期
基金：
俄罗斯基础研究基金会;
关键词：
Lattice; Metabelian group; Nilpotent group; Quasivariety of torsion-free metn groups;
D O I：
10.1023/A:1023398222909
中图分类号：
学科分类号：
摘要：
Assume that a quasivariety M of groups contains a non-Abelian free metabelian group and a non-Abelian free nilpotent group of class 2. It is proved that the lattice of quasivarieties contained in M is infinite and non-modular. © 2003 Plenum Publishing Corporation.
引用
收藏
页码：92 / 104
页数：12
相关论文
共 13 条
[1]  
Budkin A.I., Independent axiomatizability of quasivarieties of solvable groups, Algebra Logika, 30, 2, pp. 125-153, (1991)
[2]  
Budkin A.I., Quasivarieties with torsion-free nilpotent groups, Algebra Logika, 40, 6, pp. 629-650, (2001)
[3]  
Vinogradov A.A., Quasivarieties of Abelian groups, Algebra Logika, 4, 1, pp. 15-19, (1965)
[4]  
Fyodorov A.N., Quasi-identities of finite 2-nilpotent groups, 5489 -B87, (1987)
[5]  
Shakhova S.A., On a lattice of quasivarieties of nilpotent groups of class 2, Sib. Adv. Math, 7, 3, pp. 98-125, (1997)
[6]  
Budkin A.I., A lattice of quasivarieties of nilpotent groups, Algebra Logika, 33, 1, pp. 25-36, (1994)
[7]  
Budkin A.I., Gorbunov V.A., Toward a theory of quasivarieties of algebraic systems, Algebra Logika, 14, 2, pp. 123-142, (1975)
[8]  
Gorbunov V.A., Algebraic Theory of Quasivarieties, Sib. School Alg. Log, (1999)
[9]  
Mal'tsev A.I., Free solvable groups, Dokl. Akad. Nauk SSSR, 130, 3, pp. 495-498, (1960)
[10]  
Kargapolov M.I., Merzlyakov Y.I., Fundamentals of Group Theory, (1972)
12