On embeddings of countable generalized soluble groups into two-generated groups
type: Item
instance of: scholarly article
title: On embeddings of countable generalized soluble groups into two-generated groups
zbMATH Open document ID: 1006.20026
author: Vahagn H. Mikaelian
published in: Journal of Algebra
publication date: 2003-03-05T00:00:00Z
review text: 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.
reviewed by: Hermann Heineken
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F60
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1762088
zbMATH Keywords: order preserving embeddings
zbMATH Keywords: SI*-groups
zbMATH Keywords: SN*-groups
zbMATH Keywords: countable groups
zbMATH Keywords: two-generator groups
zbMATH Keywords: subnormal subgroups
MaRDI profile type: Publication
full work available at URL: jabr.2002.9047
OpenAlex ID: W2074403691
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DOI: 10.1006/JABR.2002.9047
description: scientific article; zbMATH DE number 1762088