This article is cited in 1 scientific paper (total in 1 paper)
On the closedness of a locally cyclic subgroup in a metabelian group
A. I. Budkin
Altai State University, Barnaul, Russia
The dominion of a subgroup $H$ in a group $G$ (in the class of metabelian groups) is the set of all elements $a\in G$ whose images are equal for all pairs of homomorphisms from $G$ into every metabelian group that coincide on $H$. The dominion is a closure operator on the lattice of subgroups of $G$. We study the closed subgroups with respect to the dominion. It is proved that if $G$ is a metabelian group, $H$ is a locally cyclic group, the commutant $G'$ of $G$ is the direct product of its subgroups of the form $H^f$ ($f\in G$), and $G'=H^G\times K$ for a suitable subgroup $K$; then the dominion of $H$ in $G$ coincides with $H$.
metabelian group, abelian group, dominion, closed subgroup.
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Siberian Mathematical Journal, 2014, 55:6, 1009–1016
A. I. Budkin, “On the closedness of a locally cyclic subgroup in a metabelian group”, Sibirsk. Mat. Zh., 55:6 (2014), 1240–1249; Siberian Math. J., 55:6 (2014), 1009–1016
Citation in format AMSBIB
\paper On the closedness of a~locally cyclic subgroup in a~metabelian group
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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A. I. Budkin, “Dominions in solvable groups”, Algebra and Logic, 54:5 (2015), 370–379
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