Fesenko group

In mathematics, Fesenko groups are certain subgroups of the wild automorphism groups of local fields of positive characteristic (i.e. the Nottingham group), studied by Ivan Fesenko (Fesenko (1999)).

The Fesenko group F(F_p) is a closed subgroup of the Nottingham group N(F_p) consisting of formal power series t + a₂t^1+2p+a₃t^1+3p+... with coefficients in F_p. The group multiplication is induced from that of the Nottingham group and is given by substitution.

The group multiplication is not abelian. This group is torsion free (Fesenko (1999)), unlike the Nottingham group. This group is a finitely generated pro-p-group (Fesenko (1999)) and of finite width (Griffin (2005)). It can be realized as the Galois group of an arithmetically profinite extension of local fields (Fesenko (1999)).

References

Fesenko, Ivan (1999), "On just infinite pro-p-groups and arithmetically profinite extensions of local fields", Journal für die reine und angewandte Mathematik, 517: 61–80, doi:10.1515/crll.1999.098, ISSN 0075-4102, MR 1728547
Griffin, Cornelius (2005), "The Fesenko groups have finite width", The Quarterly Journal of Mathematics, 56 (3): 337–344, doi:10.1093/qmath/hah033, ISSN 0033-5606, MR 2161247
du Sautoy, Marcus; Fesenko, Ivan (2000), "Where the wild things are: ramification groups and the Nottingham group", in du Sautoy, Marcus; Segal, Dan; Shalev, Aner, New horizons in pro-p groups, Progr. Math., 184, Boston, MA: Birkhäuser Boston, pp. 287–328, ISBN 978-0-8176-4171-9, MR 1765121

This article is issued from Wikipedia - version of the 11/5/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.