On residually finite groups and their generalizations
The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In  it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions asked in  and .