Free-by-finite pro-\(p\) groups and integral \(p\)-adic representations
type: Item
instance of: scholarly article
title: Free-by-finite pro-\(p\) groups and integral \(p\)-adic representations
zbMATH Open document ID: 1236.20033
author: Anderson L. P. Porto
author: Pavel Zalesskij
published in: Archiv der Mathematik
publication date: 2011-10-25T00:00:00Z
review text: The paper under review is a contribution to the theory of integral \(p\)-adic representations of finite \(p\)-groups. Given a free pro-\(p\) group \(F_n\) of finite rank \(n\), the natural epimorphism of \(F_n\) onto its quotient over the closure of its derived subgroup induces an epimorphism of the group \(\Aut(F_n)\) of automorphisms of \(F_n\) onto \(\text{GL}_n(\mathbb Z_p)\), where \(\mathbb Z_p\) is the ring of \(p\)-adic integers. In the main results, the authors find out which integral \(p\)-adic representations \(\rho\colon H\to\text{GL}_n(\mathbb Z_p)\) lift to a representation \(H\to\Aut(F_n)\), in the cases when \(H\) is a finite cyclic \(p\)-group, or \(H\) is a finite \(p\)-group such that for every subgroup \(C\) of \(H\) the restriction of \(\rho\) to \(C\) has no trivial indecomposable components.
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20C11
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 5963415
zbMATH Keywords: profinite groups
zbMATH Keywords: \(p\)-adic representations of finite groups
zbMATH Keywords: finite \(p\)-groups
reviewed by: Andrea Caranti
MaRDI profile type: Publication
full work available at URL: s00013-011-0294-6
OpenAlex ID: W1999522589
cites work: Q3922829
cites work: Q3922831
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cites work: Combinatorial group theory for pro-p groups
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DOI: 10.1007/S00013-011-0294-6
description: scientific article; zbMATH DE number 5963415