Quasirecognizability by the Set of Element Orders for Groups~$^3D_4(q)$ and~$F_4(q)$, for $q$~Odd

O. A. Alekseeva ; A. S. Kondrat'ev

Algebra i logika, Tome 44 (2005) no. 5, pp. 517-539.

Résumé

It is proved that if $L$ is one of the simple groups $^3D_4(q)$ or $F_4(q)$, where $q$ is odd, and $G$ is a finite group with the set of element orders as in $L$, then the derived subgroup of $G/F(G)$ is isomorphic to $L$ and the factor group $G/G'$ is a cyclic $\{2,3\}$-group.

Détail

Keywords: finite group, set of element orders, quasirecognizability, prime graph.
Mots-clés : simple group

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