Journal of the Ramanujan Mathematical Society

Volume 41, Issue 1, March 2026 pp. 9–14.

On the index divisors of certain sextic number fields

Authors: Anuj Jakhar and Ravi Kalwaniya
Author institution:Department of Mathematics, Indian Institute of Technology Madras, Chennai~600~036, India.

Summary: Let K = Q(θ) be an algebraic number field with θ a root of an irreducible quadrinomial f (x) = x6 + axm + bx + c ∈ Z[x] with m ∈ {2, 3, 4, 5}. In the present paper, we give some explicit conditions involving only a, b, c and m for which K is non-monogenic. Moreover, in each case we determine the highest powers of the primes 2 and 3 dividing the index of the field K. In particular, we provide a partial answer to the Problem 22 of Narkiewicz [10] for these number fields. Finally, we illustrate our results through examples.

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