Subgroups of the Nottingham group
type: Item
instance of: scholarly article
title: Subgroups of the Nottingham group
zbMATH Open document ID: 0883.20015
published in: Journal of Algebra
publication date: 1998-01-22T00:00:00Z
review text: The Nottingham group is defined as the subgroup of the automorphism group \(\Aut \mathbb{F}_p((t))\) of the field of formal power series, consisting of automorphisms of the form \(t\to t+\sum_{i=2}^\infty\alpha_it\). This group has received considerable attention from pro-\(p\) group theorists during the last few years, because of certain interesting properties it possesses: it is a finitely generated, just infinite pro-\(p\) group of finite width. Nevertheless, as is shown in the present paper, it is surprisingly large in the sense that every separable pro-\(p\) group can be embedded in it, as a closed subgroup.
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 1089116
zbMATH Keywords: profinite groups
zbMATH Keywords: pro-\(p\) groups
zbMATH Keywords: Nottingham group
zbMATH Keywords: automorphism groups
zbMATH Keywords: finitely generated just-infinite pro-\(p\) groups
zbMATH Keywords: separable pro-\(p\) groups
zbMATH Keywords: embeddings as closed subgroups
author: Rachel D. Camina
reviewed by: Pavel Zalesskij
MaRDI profile type: Publication
full work available at URL: jabr.1997.7082
OpenAlex ID: W2025351203
cites work: Q3997907
cites work: Substitution Groups of Formal Power Series
cites work: Q3818488
cites work: An embedding theorem for pro-finite groups
cites work: Q4891344
cites work: Q5676405
cites work: Q5566639
DOI: 10.1006/JABR.1997.7082
description: scientific article; zbMATH DE number 1089116