Let $ \pi $ be a set of primes.A finite group is said to be a $ \pi $ -group if all prime divisors of its order belong to $ \pi $ .Following Wielandt, we say that for a finite group $ G $ the $ \pi $ -Sylow theorem holds if all maximal $ \pi $ -subgroups of $ G $ are conjugate;if the $ \pi $ -Sylow theorem holds for every subgroup of $ G $ , then $ G $ is said to satisfy the strong $ \pi $ -Sylow theorem.The question of which finite nonabelian simple groups satisfy the strong $ \pi $ -Sylow theorem was posed by Wielandt in 1979.This paper completes an arithmetic description of the groups of Lie type of rank $ 1 $ that satisfy the strong $ \pi $ -Sylow theorem.
