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

2005/12/12 by Goulnara Arzhantseva, Arzhantseva, Goulnara, Pierre de la Harpe +3
Mathematics · #20E18 #20F14 #20F22 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.math/0512242

openalex publication_date 2005/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The 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.

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