A b s t r ac t. Let F be a field, A be a vector space over F and G be a subgroup of 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 K and H is not maximal in K there exists a subgroup L of finite central dimension such that H L K. In this paper we study some locally soluble linear groups with a dense family of subgroups, having finite central dimension.

We study locally solvable linear groups with a dense family of subgroups having finite central dimension.

We say that a Leibniz algebra $L$ has a dense family of ideals, if for every pair of subalgebras $A$, $B$ of $L$ such that $A\leqslant B$ and $A$ is not maximal in $B$ there exists an ideal $S$ such that $A\leqslant S\leqslant B$. We study the Leibniz algebras, having a dense family of ideals.