Large hereditarily just infinite groups.
type: Item
instance of: scholarly article
title: Large hereditarily just infinite groups.
zbMATH Open document ID: 1209.20028
author: John S. Wilson
published in: Journal of Algebra
publication date: 2010-08-11T00:00:00Z
review text: The author gives a criterion for an inverse limit of a sequence of finite groups to be hereditarily just infinite, and a similar criterion for direct limits. He then uses this criterion to give constructions of hereditarily just infinite groups which satisfy required properties. In particular, the author constructs a hereditarily just infinite profinite group in which every countably based profinite group can be embedded (Theorem A). Thus demonstrating that a hereditarily just infinite profinite group need not be virtually pro-\(p\). Secondly the author constructs hereditarily just infinite prosoluble groups that are not (topologically) finitely generated (Theorem B). This is a useful paper which provides examples of hereditarily just infinite groups which enhance our understanding of these structures.
reviewed by: Rachel D. Camina
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E26
zbMATH DE Number: 5768596
zbMATH Keywords: just infinite groups
zbMATH Keywords: profinite groups
zbMATH Keywords: pro-\(p\)-groups
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: inverse limits of finite groups
zbMATH Keywords: direct limits
zbMATH Keywords: prosoluble groups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.03.023
OpenAlex ID: W2002000072
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DOI: 10.1016/J.JALGEBRA.2010.03.023
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description: scientific article; zbMATH DE number 5768596