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Let $K$ be a number field generated by a root $\th$ of a monic irreducibletrinomial $F(x) = x^n+ax^{m}+b \in \Z[x]$. In this paper, we study the problemof $K$. More precisely, we provide some explicit conditions on $a$, $b$, $n$,and $m$ for which $K$ is not monogenic. As applications, we show that there areinfinite families of non-monogenic number fields defined by trinomials ofdegree $n=2^r\cdot3^k$ with $r$ and $k$ two positive integers. We also giveinfinite families of non-monogenic sextic number fields defined by trinomials.Some illustrating examples are giving at the end of this paper.

On index divisors and monogenity of certain number fields defined by trinomials