### Linear groups saturated by subgroups of finite central dimension

#### 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

#### Full Text:

PDFDOI: http://dx.doi.org/10.12958/adm1317

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