This article is cited 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.

MSC: Primary 20E15, 20F16; Secondary 20E25, 20E34, 20F22, 20F50

Received: 13.01.2019

Language: English

DOI: 10.12958/adm1317

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