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On Embeddings of Countable Generalized Soluble Groups into Two-Generated Groups

✍ Scribed by Vahagn H. Mikaelian

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 133 KB
Volume: 250
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2002.9047

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✦ Synopsis

Strengthening a theorem of L. G. Kovács and B. H. Neumann on embeddings of countable SN * -and SI * -groups into two-generated SN * -and SI * -groups, we establish embeddability of fully ordered countable SN-, SN * -, SI-, and SI * -groups into appropriate fully ordered two-generated groups of the same type. Moreover, for an arbitrary non-trivial word set V ⊆ F ∞ the mentioned two-generated group can be chosen such that the verbal V -subgroup of the latter contains the order isomorphic copy of an initial countable group. These embeddings are subnormal but not, in general, normal.  2002 Elsevier Science (USA)

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