On the Residual Finiteness of a Class of Infinite Soluble Groups

Abstract

Let [Formula: see text] be a completely decomposable homogeneous torsion-free abelian group of rank [Formula: see text] ([Formula: see text]). Let [Formula: see text] be the split extension of [Formula: see text] by an automorphism [Formula: see text] which is a cyclic permutation of the direct components twisted by a rational integer [Formula: see text]. Then [Formula: see text] is an infinite soluble group. In this paper, the residual finiteness of [Formula: see text] is investigated.