Author:
SNOPCE ILIR,ZALESSKII PAVEL A.
Abstract
AbstractWe prove that a non-solvable Demushkin group satisfies the Greenberg–Stallings property, i.e., if H and K are finitely generated subgroups of a non-solvable Demushkin group G with the property that H ∩ K has finite index in both H and K, then H ∩ K has finite index in 〈H, K〉. Moreover, we prove that every finitely generated subgroup H of G has a ‘root’, that is a subgroup K of G that contains H with |K : H| finite and which contains every subgroup U of G that contains H with |U : H| finite. This allows us to show that every non-trivial finitely generated subgroup of a non-solvable Demushkin group has finite index in its commensurator.
Publisher
Cambridge University Press (CUP)
Reference15 articles.
1. Finite index and finite codimension
2. Sur la dimension cohomologique des groupes profinis
3. Infiniteness of the number of relations in a Galois group of maximal p-extensions with a bounded ramification of a local field;Gordeev;Izv. Ross. Acad. NaukSer. Mat.,1981
4. Pro-p
groups of positive deficiency
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