Harrington and Jones characterized monogenity of four new parametric families of quartic polynomials with various Galois groups. A short time later Voutier added a cyclic family. In this note, we intend to describe all generators of power integral bases in the number fields generated by a root of the monogenic polynomials.

power integral basis, quartic fields, Thue equations.

Received: November 6, 2024; Revised: November 24, 2024; Accepted: December 5, 2024; Published: December 17, 2024

How to cite this article: István Gaál, Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials, JP Journal of Algebra, Number Theory and Applications 64(1) (2025), 99-115. https://doi.org/10.17654/0972555525006

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