Geodesic
A characterization of simple Zassenhaus groups
Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 397-409 
A. V. Romanovskii. A characterization of simple Zassenhaus groups. Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 397-409. http://geodesic.mathdoc.fr/item/SM_1984_47_2_a8/
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     author = {A. V. Romanovskii},
     title = {A~characterization of simple {Zassenhaus} groups},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_47_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let a finite group $G$ have a $CC$-subgroup $M$ of order $m$ whose normalizer differs from $M$ and $G$, and let the order of $N_G(M)$ be odd and each coset $Mx$ of $G$, for $x\in G\setminus N_G(M)$, contain an involution. Earlier the author (R Zh Mat, 1979, 8A154) posed the question of the existence of simple groups other than $PSL(2,m)$ with the indicated properties. In this paper it is proved that $G\cong PSL(2,m)$. The result includes theorems of Feit and Ito on Zassenhaus groups. Bibliography: 11 titles.

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[11] Ito N., “On a class of doubly transitive permutation groups”, Illinois J. Math., 6:2 (1962), 341–352 | MR | Zbl