Explicit discriminant of a class of polynomial, monogenity and Galois group

Authors

• Anuj Jakhar, Indian Institute of Technology Madras
• Shanta Laishram, Indian Statistical Institute (Delhi Centre)
• Prabhakar Yadav, Indian Statistical Institute (Delhi Centre)

Article Type

Research Article

Publication Title

Communications in Algebra

Abstract

Let (Formula presented.) where (Formula presented.) is a root of an irreducible polynomial (Formula presented.) = (Formula presented.), (Formula presented.) and (Formula presented.) denote the ring of algebraic integers of K. In this paper, we explicitly compute the discriminant of (Formula presented.) and provide necessary and sufficient conditions involving only a, b, m, k, n for (Formula presented.) to be monogenic. Moreover, we characterize all the primes dividing the index of the subgroup (Formula presented.) in (Formula presented.). As an application, we also provide a class of monogenic polynomials having non square-free discriminant and Galois group (Formula presented.), the permutation group on n letters.

First Page

2937

Last Page

2948

DOI

10.1080/00927872.2025.2451106

Publication Date

1-1-2025

Recommended Citation

Jakhar, Anuj; Laishram, Shanta; and Yadav, Prabhakar, "Explicit discriminant of a class of polynomial, monogenity and Galois group" (2025). Journal Articles. 5352.
https://digitalcommons.isical.ac.in/journal-articles/5352