International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 2, Pages 65-76
doi:10.1155/S0161171204211280
On embedding properties of SD-groups
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.
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.