Addendum: Π-principal hereditary orders (Nagoya Math. J. 32 (1968), 41–65)

Abstract

Let R denote a complete discrete rank one valuation ring of unequal characteristic, and let p denote the characteristic of the residue class field R̅ of R. Consider the integral closure S of R in a finite Galois extension K of the quotient field k of R. Recall (see Prop. 1.1 of [3]) that the inertia group G0 of K over k is a semi-direct product G0 = J × Gp, where J is a cyclic group of order relatively prime to p and Gp is a normal p-subgroup of G.