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Conjecture $\mathbb{Z}$ is a knot theoretical equivalent form of the KervaireConjecture. We say that a knot have property $\mathbb{Z}$ if it satisfiesConjecture $\mathbb{Z}$ for that specific knot. In this work, we show thatalternating Montesinos knots with three tangles have property $\mathbb{Z}$. Wealso show that all the pretzel knots of the form $P(p,q,r)$ (not necessarilyalternating) have property $\mathbb{Z}$.

Alternating Montesinos knots and Conjecture $\mathbb{Z}$