Let $ \pi $ be a set of primes. A finite group $ G $ is a $ \pi $ -group if allprime divisors of the order of $ G $ belong to $ \pi $ . Following Wielandt,the $ \pi $ -Sylow theorem holds for $ G $ if all maximal $ \pi $ -subgroups of $ G $ are conjugate; if the $ \pi $ -Sylow theorem holds forevery subgroup of $ G $ then the strong $ \pi $ -Sylow theorem holdsfor $ G $ . The strong $ \pi $ -Sylow theorem is known to hold for $ G $ if and only if it holds for every nonabelian composition factor of $ G $ .In 1979, Wielandt asked which finite simple nonabelian groups obey the strong $ \pi $ -Sylow theorem.By now the answer isknown for sporadic and alternating groups. We give somearithmetic criterion for the validity of the strong $ \pi $ -Sylow theorem forthe groups $ \operatorname{PSL}_{2}(q) $ .
