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Sibirsk. Mat. Zh., 2018, Volume 59, Number 4, Pages 759–772 (Mi smj3008)  

On dominions of the rationals in nilpotent groups

A. I. Budkin

Altai State University, Barnaul, Russia

Abstract: The dominion of a subgroup $H$ of a group $G$ in a class $M$ is the set of all $a\in G$ 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 $G=\operatorname{gr}(H,a_1,…,a_n)$ 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 $3$.

Keywords: quasivariety, nilpotent group, additive group of the rationals, dominion, $2$-closed group.

DOI: https://doi.org/10.17377/smzh.2018.59.403

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English version:
Siberian Mathematical Journal, 2018, 59:4, 598–609

Bibliographic databases:

UDC: 512.57
Received: 18.11.2017

Citation: A. I. Budkin, “On dominions of the rationals in nilpotent groups”, Sibirsk. Mat. Zh., 59:4 (2018), 759–772; Siberian Math. J., 59:4 (2018), 598–609

Citation in format AMSBIB
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\paper On dominions of the rationals in nilpotent groups
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