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LetRdenote a complete discrete rank one valuation ring of unequal characteristic, and letpdenote the characteristic of the residue class fieldR̅ofR. Consider the integral closureSofRin a finite Galois extensionKof the quotient fieldkofR. Recall (see Prop. 1.1 of ) that the inertia groupG0ofKoverkis a semi-direct productG0= J × Gp, whereJis a cyclic group of order relatively prime topandGpis a normalp-subgroup of G.doi:10.1017/s0027763000024685 fatcat:zvqezlvilnfitph6mffzh7amcu