群的真可解完备化：实例与开放问题
The true prosoluble completion of a group: examples and open problems
摘要：
群$Γ$的真预可解完备化$P\Cal S (Γ)$是$Γ$的可解子的投射系的逆极限。我们的目的是描述例子，并指出一些自然的开放问题。本文讨论了一个关于Profinite完备化的Grothendieck问题及其在真Prosoluble和真Pronilpotent完备化中的类似问题。1.导论. 2.关于有向正规子群集的完备化。3.泛性质。4.正规子群的有向集的例子。5.真正的prosoluble完成。6.例子. 7.关于Grothendieck问题的真prosoluble和真pronilpotent类似物。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
