$SD$-Groups and Embeddings

Abstract

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 also be fully ordered. For any non-trivial 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 $H$.