Geodesic
On Finite Simple Groups with the Set of Element Orders as in a Frobenius Group or a Double Frobenius Group
Matematičeskie zametki, Tome 73 (2003) no. 3, pp. 323-339

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It is proved that a finite simple group with the set of element orders as in a Frobenius group (a double Frobenius group, respectively) is isomorphic to $L_3(3)$ or $U3_(3)$ (to $U_3(3)$ or $S_4(3)$, respectively). 
@article{MZM_2003_73_3_a0,
     author = {M. R. Aleeva},
     title = {On {Finite} {Simple} {Groups} with the {Set} of {Element} {Orders} as in a {Frobenius} {Group} or a {Double} {Frobenius} {Group}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--339},
     publisher = {mathdoc},
     volume = {73},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_3_a0/}
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M. R. Aleeva. On Finite Simple Groups with the Set of Element Orders as in a Frobenius Group or a Double Frobenius Group. Matematičeskie zametki, Tome 73 (2003) no. 3, pp. 323-339. http://geodesic.mathdoc.fr/item/MZM_2003_73_3_a0/