Indices of inseparability for elementary abelian p-extensions

Let K be a local field whose residue field K¯ is a finite field of characteristic p and let L/K be a finite totally ramified Galois extension. Fried [3] and Heiermann [5] defined the “indices of inseparability” of L/K, a refinement of the ramification data of L/K. We give a method for computing the indices of inseparability of the extension L/K in terms of the norm group NL/K(L×) in the case where K has characteristic p and Gal(L/K) is an elementary abelian p-group with a single ramification break. In some cases our methods lead to simple formulas for the indices of inseparability.