The wild inertia subgroup 
of a finite Galois extension
of local fields with residue
characteristic 
is the first higher ramification group 
. It is the unique Sylow
p-subgroup of the inertia subgroup.
The quotient group of the inertia
subgroup by 
is a cyclic group of order prime to 
.
Wild Inertia Subgroup
See also
Inertia Subgroup, Ramification Group, Tame Ramification, Wild RamificationExplore with Wolfram|Alpha
References
Serre, J.-P. Local Fields. New York: Springer-Verlag, 1979.Cite this as:
Weisstein, Eric W. "Wild Inertia Subgroup." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WildInertiaSubgroup.html