Linear groups saturated by subgroups of finite central dimension

Abstract

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.

Leibniz algebras, having a dense family of ideals

“…This topic is not limited to the framework of the classical theory of groups. For example, in [24] the infinite dimensional linear groups having a dense family of subgroups of finite central dimension were considered.…”