Geodesic
Linear groups saturated by subgroups of finite central dimension
Algebra and discrete mathematics, Tome 29 (2020) no. 1, pp. 117-128.

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Let $F$ be a field, $A$ be a vector space over $F$ and $G$ be a subgroup of $\mathrm{GL}(F,A)$. We say that $G$ has a dense family of subgroups, having finite central dimension, if for every pair of subgroups $H$, $K$ of $G$ such that $H\leqslant K$ and $H$ is not maximal in $K$ there exists a subgroup $L$ of finite central dimension such that $H\leqslant L\leqslant K$. In this paper we study some locally soluble linear groups with a dense family of subgroups, having finite central dimension.
Keywords: linear group, infinite group, infinite dimensional linear group, dense family of subgroups, locally soluble group, finite central dimension. 
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N. N. Semko; L. V. Skaskiv; O. A. Yarovaya. Linear groups saturated by subgroups of finite central dimension. Algebra and discrete mathematics, Tome 29 (2020) no. 1, pp. 117-128. http://geodesic.mathdoc.fr/item/ADM_2020_29_1_a10/

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