Prographes sylvestres et groupes profinis presque libres

In this article we want to give an analogous in the profinite case to the following theorem: an abstract group is free if and only if it acts freely on a tree. In a first time we define a combinatory object, the protrees, which are particular inductive systems extracted from projective systems of gr...

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Bibliographic Details
Published inMathematische annalen Vol. 350; no. 2; pp. 475 - 495
Main Authors Deschamps, Bruno, Suarez Atias, Ivan
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.06.2011
Springer Verlag
Subjects
Mathematics
Mathematics and Statistics
Number Theory
20E99
Primary 20E18
20E08
05C99
Secondary 05C05
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Summary:In this article we want to give an analogous in the profinite case to the following theorem: an abstract group is free if and only if it acts freely on a tree. In a first time we define a combinatory object, the protrees, which are particular inductive systems extracted from projective systems of graphs. Then we define a notion of profinite action . These objects allow us to give the following analogous: a profinite group contains a dense abstract free subgroup if and only if it acts profreely on a protree.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-010-0566-7