On embedding properties of S D -groups

Vahagn H. Mikaelian

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-12

Abstract:

Continuing our recent research on embedding properties of generalized soluble and generalized nilpotent groups, we study some embedding properties of S D -groups. We show that every countable S D -group G can be subnormally embedded into a two-generator S D -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 S D -groups which are not locally soluble.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:505214

DOI: 10.1155/S0161171204211280

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