$SD$-Groups and Embeddings
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...
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2008-12-01
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| Series: | Armenian Journal of Mathematics |
| Online Access: | http://armjmath.sci.am/index.php/ajm/article/view/43 |
| Summary: | 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 $H$.
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| ISSN: | 1829-1163 |