Groups with a dense system of complemented nonextremal Abelian subgroups

Suppose $G$ is a group containing nonextremal Abelian subgroups. We say that it possesses a dense system of complemented nonextremal Abelian subgroups if for any two nonextremal Abelian subgroups $A\subset B$ of $G$, the first of which is not maximal in the second, there exists a $G$-complemented subgroup contained strictly between them. In this paper we obtain a description of the locally finite groups with such a dense system of subgroups. In particular, all infinite Abelian subgroups of such groups are complemented.