On embeddings of countable generalized soluble groups into two-generated groups (Q1602009)
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scientific article; zbMATH DE number 1762088
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On embeddings of countable generalized soluble groups into two-generated groups |
scientific article; zbMATH DE number 1762088 |
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On embeddings of countable generalized soluble groups into two-generated groups (English)
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5 March 2003
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Well-known results of B. H. Neumann, H. Neumann and G. Higman state that a countable group can be embedded into a two-generator group. B. H. Neumann and L. G. Kovács have also shown that this is possible within the class of SI* (SN*)-groups. The author shows that it is also possible to embed the countable group as a subnormal subgroup (also within the classes of SI (SN)-groups). The length of the normal (subnormal) series in the case of SI* (SN*)-groups can be made to increase only by 2, and orders can be preserved.
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order preserving embeddings
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SI*-groups
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SN*-groups
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countable groups
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two-generator groups
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subnormal subgroups
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