On just infinite propgroups and arithmetically profinite extensions of local fields
Abstract
The wild group is the group of wild automorphisms of a local field of characteristic p. In this paper we apply FontaineWintenberger's theory of fields of norms to study the structure of the wild group. In particular we provide a new short proof of R. Camina's theorem which says that every propgroup with countably many open sugroups is isomorphic to a closed subgroup of the wild group. We study some closed subgroups T of the wild group whose commutator subgroup is unusually small. Realizing the group T as the Galois group of arithmetically profinite extensions of padic fields we answer affirmatively CoatesGreenberg's problem on deeply ramified extensions of local fields. Finally using the subgroup T we show that the wild group is not analytic over commutative complete local noetherian integral domains with finite residue field of characteristic p.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1998
 DOI:
 10.48550/arXiv.math/9802092
 arXiv:
 arXiv:math/9802092
 Bibcode:
 1998math......2092F
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Number Theory;
 11S15;
 20F99;
 22E99
 EPrint:
 15 pages, AMSTeX