Summary: Geom Dedicata
DOI 10.1007/s107110069103y
ORIGINAL PAPER
The true prosoluble completion of a group: Examples
and open problems
Goulnara Arzhantseva · Pierre de la Harpe ·
Delaram Kahrobaei · Zoran Suni´c
Received: 5 January 2006 / Accepted: 5 October 2006
© Springer Science+Business Media B.V. 2006
Abstract The true prosoluble completion PS( ) of a group is the inverse limit of
the projective system of soluble quotients of . 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
