Resumen de The {ie210-01}-property in finite simple groups

D. O. Revin

• Let ? be some set of primes. A finite group is said to possess the {ie210-02}-property if all of its maximal ?-subgroups are conjugate. It is not hard to show that this property is equivalent to satisfaction of the complete analog of Sylow's theorem for Hall ?-subgroups of a group. In the paper, we bring to a close an arithmetic description of finite simple groups with the {ie210-03}-property, for any set ? of primes. Previously, it was proved that a finite group possesses the {ie210-04}-property iff each composition factor of the group has this property. Therefore, the results obtained mean in fact that the question of whether a given group enjoys the {ie210-05}-property becomes purely arithmetic.