$SD$-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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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 |
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doaj-a69a6771f0b546a6a51ae78495e8272c2020-11-25T02:34:02ZengRepublic of Armenia National Academy of SciencesArmenian Journal of Mathematics1829-11632008-12-0113$SD$-Groups and EmbeddingsVahagn Mikaelian0Yerevan State University, Yerevan, Armenia 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 $H$. http://armjmath.sci.am/index.php/ajm/article/view/43 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Vahagn Mikaelian |
| spellingShingle |
Vahagn Mikaelian $SD$-Groups and Embeddings Armenian Journal of Mathematics |
| author_facet |
Vahagn Mikaelian |
| author_sort |
Vahagn Mikaelian |
| title |
$SD$-Groups and Embeddings |
| title_short |
$SD$-Groups and Embeddings |
| title_full |
$SD$-Groups and Embeddings |
| title_fullStr |
$SD$-Groups and Embeddings |
| title_full_unstemmed |
$SD$-Groups and Embeddings |
| title_sort |
$sd$-groups and embeddings |
| publisher |
Republic of Armenia National Academy of Sciences |
| series |
Armenian Journal of Mathematics |
| issn |
1829-1163 |
| publishDate |
2008-12-01 |
| description |
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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http://armjmath.sci.am/index.php/ajm/article/view/43 |
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AT vahagnmikaelian sdgroupsandembeddings |
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