BourbakiV1, Istex, Corpus, bibRecord, 000D56

The true prosoluble completion of a group: Examples and open problems

Identifieur interne : 000D56 ( Istex/Corpus ); précédent : 000D55; suivant : 000D57

The true prosoluble completion of a group: Examples and open problems

Auteurs : Goulnara Arzhantseva ; Pierre De La Harpe ; Delaram Kahrobaei ; Zoran Šuni

Source :

Geometriae Dedicata [ 0046-5755 ] ; 2007-02-01.

RBID : ISTEX:42902F41A52C53E51EFF4B96C1E828A7C0AE8A4B

English descriptors

KwdEn :
- Grigorchuk group, Open problems, Profinite completion, Residual properties, Soluble group, True prosoluble completion.

Abstract

Abstract: The true prosoluble completion $$P\mathcal S (\Gamma)$$ of a group Γ is the inverse limit of the projective system of soluble quotients of Γ. Our purpose is to describe examples and to point out some natural open problems. We discuss a question of Grothendieck for profinite completions and its analogue for true prosoluble and true pronilpotent completions.

Url:

https://api.istex.fr/document/42902F41A52C53E51EFF4B96C1E828A7C0AE8A4B/fulltext/pdf

DOI: 10.1007/s10711-006-9103-y

Links to Exploration step

ISTEX:42902F41A52C53E51EFF4B96C1E828A7C0AE8A4B

Le document en format XML

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<Para>The <Emphasis Type="Italic">true prosoluble completion</Emphasis>
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<EquationSource Format="TEX">$$P\mathcal S (\Gamma)$$</EquationSource>
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 of a group Γ is the inverse limit of the projective system of soluble quotients of Γ. Our purpose is to describe examples and to point out some natural open problems. We discuss a question of Grothendieck for profinite completions and its analogue for true prosoluble and true pronilpotent completions.</Para>
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<KeywordGroup Language="En"><Heading>Keywords</Heading>
<Keyword>Soluble group</Keyword>
<Keyword>Residual properties</Keyword>
<Keyword>True prosoluble completion</Keyword>
<Keyword>Profinite completion</Keyword>
<Keyword>Open problems</Keyword>
<Keyword>Grigorchuk group</Keyword>
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<Keyword>20F22</Keyword>
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<ArticleNote Type="Misc"><SimplePara>Goulnara Arzhantseva and Zoran Šunić were the authors of the Appendix.</SimplePara>
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<name type="personal" displayLabel="corresp"><namePart type="given">Goulnara</namePart>
<namePart type="family">Arzhantseva</namePart>
<affiliation>Section de Mathématiques, Université de Genève, C.P. 64, CH-1211, Geneva, Switzerland</affiliation>
<affiliation>E-mail: goulnara.arjantseva@math.unige.ch</affiliation>
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<name type="personal"><namePart type="given">Pierre</namePart>
<namePart type="family">de la Harpe</namePart>
<affiliation>Section de Mathématiques, Université de Genève, C.P. 64, CH-1211, Geneva, Switzerland</affiliation>
<affiliation>E-mail: pierre.delaharpe@math.unige.ch</affiliation>
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<name type="personal"><namePart type="given">Delaram</namePart>
<namePart type="family">Kahrobaei</namePart>
<affiliation>Mathematics Department (Namm 724), New York City College of Technology (CUNY), 300 Jay Street, 11201, Brooklyn, NY, USA</affiliation>
<affiliation>E-mail: DKahrobaei@CityTech.CUNY.edu</affiliation>
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<name type="personal"><namePart type="given">Zoran</namePart>
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<abstract lang="en">Abstract: The true prosoluble completion $$P\mathcal S (\Gamma)$$ of a group Γ is the inverse limit of the projective system of soluble quotients of Γ. Our purpose is to describe examples and to point out some natural open problems. We discuss a question of Grothendieck for profinite completions and its analogue for true prosoluble and true pronilpotent completions.</abstract>
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<subject lang="en"><genre>Keywords</genre>
<topic>Soluble group</topic>
<topic>Residual properties</topic>
<topic>True prosoluble completion</topic>
<topic>Profinite completion</topic>
<topic>Open problems</topic>
<topic>Grigorchuk group</topic>
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<dateIssued encoding="w3cdtf">2007-06-18</dateIssued>
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<subject><genre>Mathematics</genre>
<topic>Geometry</topic>
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<part><date>2007</date>
<detail type="issue"><title>Geometric and Probabilistic Methods in Group Theory and Dynamical Systems</title>
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<detail type="volume"><number>124</number>
<caption>vol.</caption>
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The true prosoluble completion of a group: Examples and open problems

The true prosoluble completion of a group: Examples and open problems

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