On Indices of Septic Number Fields Defined by Trinomials x7 + ax + b

Abstract

Let K be a septic number field generated by a root, α, of an irreducible trinomial, x7+ax+b∈Z[x]. In this paper, for every prime integer, p, we calculate νp(i(K)); the highest power of p dividing the index, i(K), of the number field, K. In particular, we calculate the index, i(K). In application, when the index of K is not trivial, then K is not monogenic.