On index divisors and monogenity of certain number fields defined by x12+axm+b

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Abstract In this paper, we study the monogenity of any number field defined by a monic irreducible trinomial F(x) = x12 + axm + b ∈ Z[x] with 1 ≤ m ≤ 11 {an integer. For every integer m, we give sufficient conditions on a and b so that the field index i(K) is not trivial. In particular, if i(K) ≠ 1, then K is not monogenic. For m=1, we give necessary and sufficient conditions on a and b, which characterize when a rational prime p divides the index i(K). For every prime divisor p of i(K), we also calculate the highest power p dividing i(K), in such a way we answer the problem 22 of Narkiewicz [20] for the number fields defined by trinomials x12+ax+b. 2010 Mathematics Subject Classification. 11R04, 11Y40, 11R21.

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