Geodesic
On the Mazurov conjecture
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 8-13

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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. 
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     title = {On the {Mazurov} conjecture},
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V. A. Antonov; S. G. Chekanov. On the Mazurov conjecture. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 8-13. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a1/