1 results
Common index divisor of the number fields defined by $x^5+\,ax\,+b$
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 4 / November 2022
- Published online by Cambridge University Press:
- 01 December 2022, pp. 1147-1161
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- Article
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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.
