International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 1-4, Pages 65-76
doi:10.1155/S0161171204211280

On embedding properties of SD-groups

Abstract

Continuing our recent research on embedding properties of generalized soluble and generalized nilpotent groups, we study some embedding properties of SD-groups. We show that every countable SD-group G can be subnormally embedded into a two-generator SD-group H. This embedding can have additional properties: if the group G is fully ordered, then the group H can be chosen to be also fully ordered. For any nontrivial word set V, this embedding can be constructed so that the image of G under the embedding lies in the verbal subgroup V(H) of H. The main argument of the proof is used to build continuum examples of SD-groups which are not locally soluble.