On the Mazurov conjecture

A conjecture by V. D. Mazurov states that if, in a $2$-Frobenius group $G=P\lambda(\langle x\rangle\lambda\langle y\rangle)$ of type $(p,q,r)$, the subgroup $C_P(y)$ is of exponent $p$ then $Exp(P)=p$. In [1] this conjecture is proved for $2$-Frobenius groups of type $(3,5,2)$. In this paper a counterexample to Mazurov's conjecture is constructed.