Characterization of primes dividing the index of a trinomial

Abstract

LetAKdenote the ring of algebraic integers of an algebraic number fieldK=Q(θ),whereθis a root of an irreducible trinomialF(x)=xn+axm+bbelonging toZ[x].In this paper, we give necessary and sufficient conditions involving onlya, b, m, nfor agiven primepto divide the index of the subgroupZ[θ]inAK. In particular, we deducenecessary and sufficient conditions forAKto be equal toZ[θ]