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Common index divisor of the number fields defined by $x^5+\,ax\,+b$![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230405131301764-0166:S0013091522000529:S0013091522000529_inline1.png)
Published online by Cambridge University Press: 01 December 2022
Abstract
Let $K={\mathbf {Q}}(\theta )$ be an algebraic number field with $\theta$
a root of an irreducible polynomial $x^5+ax+b\in {\mathbf {Z}}[x]$
. In this paper, for every rational prime $p$
, we provide necessary and sufficient conditions on $a,\,~b$
so that $p$
is a common index divisor of $K$
. In particular, we give sufficient conditions on $a,\,~b$
for which $K$
is non-monogenic. We illustrate our results through examples.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 4 , November 2022 , pp. 1147 - 1161
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
References
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![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230405131301764-0166:S0013091522000529:S0013091522000529_inline1320.png?pub-status=live)
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