International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 65-76

On embedding properties of SD-groups

Vahagn H. Mikaelian

Department of Computer Science, Yerevan State University, Yerevan 375025, Armenia

Received 19 November 2002

To the memory of Professor Alexey Ivanovich Kostrikin

Copyright © 2004 Vahagn H. Mikaelian. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.