Geodesic
A~characterization of simple Zassenhaus groups
Sbornik. Mathematics, Tome 47 (1984) no. 2, pp. 397-409

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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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     author = {A. V. Romanovskii},
     title = {A~characterization of simple {Zassenhaus} groups},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_47_2_a8/}
}
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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/