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(Fp) is a closed subgroup of the Nottingham group N(Fp) consisting of formal power series t + a2t1+2p+a3t1+3p+... with coefficients in Fp. 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)).