Indices of inseparability and refined ramification breaks

Let K be a finite extension of Qp which contains a primitive pth root of unity ζp. Let L/K be a totally ramified (Z/pZ)2-extension which has a single ramification break b. In [2] Byott and Elder defined a “refined ramification break” b⁎ for L/K. In this paper we prove that if p>2 and the index of inseparability i1 of L/K is not equal to p2b−pb then b⁎=i1−p2b+pb+b.