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December 2020 On primes dividing the index of a quadrinomial
Anuj Jakhar
Rocky Mountain J. Math. 50(6): 2117-2125 (December 2020). DOI: 10.1216/rmj.2020.50.2117

Abstract

Let K denote the ring of algebraic integers of an algebraic number field K=(𝜃) where the algebraic integer 𝜃 is a root of an irreducible quadrinomial f(x)=xn+axn1+bxn2+c belonging to [x] with a2=4b. We give necessary and sufficient conditions involving only a,b,c,n for a prime p to divide the index of the subgroup [𝜃] in K. As a consequence, we obtain necessary and sufficient conditions for K to be equal to [𝜃]. Moreover, when K[𝜃], we provide an explicit formula for the index [K:[𝜃]] in some cases.

Citation

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Anuj Jakhar. "On primes dividing the index of a quadrinomial." Rocky Mountain J. Math. 50 (6) 2117 - 2125, December 2020. https://doi.org/10.1216/rmj.2020.50.2117

Information

Received: 29 April 2020; Revised: 11 May 2020; Accepted: 11 May 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2117

Subjects:
Primary: 11R04, 11R29

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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