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

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

2005-12-12

arxiv.org/abs/math/0512242v2

Mathematics

Group Theory

15 pages; A revised version: Proposition 1 was wrong in the first version of the paper

Scientific paper

The true prosoluble completion $P\Cal S (\Gamma)$ of a group $\Gamma$ is the inverse limit of the projective system of soluble quotients of $\Gamma$. 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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