The inertia subgroup of a finite Galois extension 
of local
fields is the kernel of the homomorphism
from 
to the Galois group of the corresponding extension
of residue fields. It is a normal
subgroup of 
and is the zeroth ramification group 
.
The inertia subgroup contains the wild inertia subgroup 
.
The quotient group 
is a cyclic group of
order prime to the residue characteristic.
