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It is proved that the braid monodromy group $\Gamma_{P(z)}$ of a polynomial$P(z)\in\mathbb C[z]$, $\deg P(z)=n$, is the braid group $\text{Br}_n$ if thepolynomial $P(z)$ has $n-1$ distinct critical values.

On the braid monodromy group of a polynomial in one variable