On Dominions of the Rationals in Nilpotent Groups

Сибирский математический журнал

A. I. Budkin¹ 

[1] Altai State University

关键词: quasivariety;    nilpotent group;    additive group of the rationals;    dominion;    2-closed group;   

DOI  :  10.1134/S0037446618040031

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

The dominion of a subgroup H of a group G in a class M is the set of all a ∈ G that have the same images under every pair of homomorphisms, coinciding on H from G to a group in M. A group H is n-closed in M if for every group G = gr(H, a1,..., an) in M that includes H and is generated modulo H by some n elements, the dominion of H in G (in M) is equal to H. We prove that the additive group of the rationals is 2-closed in every quasivariety of torsion-free nilpotent groups of class at most 3.

【 授权许可】

CC BY