Geodesic
Generating triples of conjugate involutions for finite simple groups
Algebra i logika, Tome 62 (2023) no. 5, pp. 569-592.

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It is proved that among finite simple non-Abelian groups, only the groups $U_3(3)$ and $A_8$ are not generated by three conjugate involutions. This result is obtained modulo a known conjecture on the description of finite simple groups generated by two elements of orders 2 and 3.
Keywords: finite simple group, generating triples of conjugate involutions, characters of a group. 
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M. A. Vsemirnov; Ya. N. Nuzhin. Generating triples of conjugate involutions for finite simple groups. Algebra i logika, Tome 62 (2023) no. 5, pp. 569-592. http://geodesic.mathdoc.fr/item/AL_2023_62_5_a0/

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