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On common index divisor and monogenity of certain number fields defined by trinomials X⁶ + AX + B

Quaestiones Mathematicae, 2022
For a number field K defined by a trinomial F(x) = x6 + ax + b ∈ Z[x],Jakhar and Kumar gave some necessary conditions on a and b, which guarantee the non-monogenity of K [25]. In this paper, for every prime integer p, we characterize when p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic.
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On common index divisors and not monogenity of nonic number fields defined by trinomials of type $$x^9+ax+b$$

Boletín de la Sociedad Matemática Mexicana
In this paper, for a nonic number field $K$ generated by a complex root of an irreducible trinomial $F(x)=x^9+ax+b\in {\mathbb Z}[x]$, the authors characterize the case where a given prime integer $p$ divides the index of the number field $K$. More precisely, they show that if $p\ge 5$, then $p$ does not divide $i(K)$.
Hamid Ben Yakkou, Pagdame Tiebekabe
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On common index divisors and monogenity of septic number fields defined by trinomials of type $$x^7+ax^2+b$$

Acta Mathematica Hungarica
The author studies the field index $i(K)$ and monogenity properties of number fields $K$ generated by a root of an irreducible trinomial $x^7+ax^2+b$. It is shown that 2 can be the only prime divisor of $i(K)$. Necessary and sufficient conditions are given for $a,b$ so that 2 divides $i(K)$.
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On common index divisors and monogenity of certain number fields defined by x⁵ + ax² + b