Geodesic
On the Mazurov conjecture
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 8-13 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Antonov V. A., Chekanov S. G., “O dvoinykh gruppakh Frobeniusa”, Trudy inst. mat. i mekh. UrO RAN, 13, no. 1, 2007, 1–8 | MR

[2] Aleeva M. R., “O konechnykh prostykh gruppakh s mnozhestvom poryadkov elementov kak u gruppy Frobeniusa ili dvoinoi gruppy Frobeniusa”, Matematicheskie zametki, 73:3 (2003), 323–339 | MR | Zbl

[3] Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A., An atlas of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[4] Antonov V. A., Chekanov S. G., “O dvoinykh gruppakh Frobeniusa, 2”, Mezhdun. konf. “Algebra i ee prilozheniya”. Tezisy dokl. (Krasnoyarsk, 2007), 10

[5] Huppert B., Endliche Gruppen, v. 1, Springer-Verlag, Berlin, Heidelberg, New York, 1967 | MR | Zbl