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

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dc.creatorArzhantseva, Goulnara
dc.creatorde la Harpe, Pierre
dc.creatorKahrobaei, Delaram
dc.date2005-12-12
dc.date2006-05-07
dc.date.accessioned2026-07-07T06:55:05Z
dc.date.available2026-07-07T06:55:05Z
dc.descriptionThe true prosoluble completion $P\Cal S (Γ)$ 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. 1. Introduction. 2. Completion with respect to a directed set of normal subgroups. 3. Universal property. 4. Examples of directed sets of normal subgroups. 5. True prosoluble completions. 6. Examples. 7. On the true prosoluble and the true pronilpotent analogues of Grothendieck's problem.
dc.description15 pages; A revised version: Proposition 1 was wrong in the first version of the paper
dc.identifierhttps://arxiv.org/abs/math/0512242
dc.identifierhttp://arxiv.org/abs/math/0512242
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106170
dc.subjectGroup Theory
dc.subject20E18; 20F14; 20F22
dc.titleThe true prosoluble completion of a group: examples and open problems
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