On Certain Closed Normal Subgroups of Free Profinite Groups of Countably Infinite Rank

Let F be a free profinite group of countably infinite rank and (Δ) the class of all finite groups whose composition factors are in Δ for a non-empty class Δ of finite simple groups. Let R Δ (F) be the intersection of all open normal subgroups N of F such that F/N is in (Δ). Then we prove that, if is...

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Bibliographic Details
Published in:Communications in algebra 2004-12, Vol.32 (8), p.3257-3262
Main Author: Ohtani, Sachiko
Format: Article
Language:English
Subjects:
Embedding problems
Profinite groups
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Summary:Let F be a free profinite group of countably infinite rank and (Δ) the class of all finite groups whose composition factors are in Δ for a non-empty class Δ of finite simple groups. Let R Δ (F) be the intersection of all open normal subgroups N of F such that F/N is in (Δ). Then we prove that, if is the class of finite groups which have no non-trivial (Δ)-quotient, then R Δ (F) is a pro- group of countable rank and every finite -embedding problem for R Δ (F) is solvable.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120039290