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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Linear groups saturated by subgroups of finite central dimension
N. N. Semko, L. V. Skaskiv, O. A. Yarovaya Department of Mathematics, University of State Fiscal Service of Ukraine, Universytetska street 31, Irpin, Kyiv region, Ukraine
Abstract:
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.
Received: 13.01.2019
Citation:
N. N. Semko, L. V. Skaskiv, O. A. Yarovaya, “Linear groups saturated by subgroups of finite central dimension”, Algebra Discrete Math., 29:1 (2020), 117–128
Linking options:
https://www.mathnet.ru/eng/adm744 https://www.mathnet.ru/eng/adm/v29/i1/p117
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