4 research outputs found
On embedding properties of SD-groups
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