Confirmation for Wielandt's conjecture

Let π be a set of primes. By H. Wielandt's definition, Sylow π-theorem holds for a finite group G if all maximal π-subgroups of G are conjugate. In the paper, the following statement is proven. Assume that π is a union of disjoint subsets σ and τ and a finite group G possesses a π-Hall subgroup which is a direct product of a σ-subgroup and a τ-subgroup. Furthermore, assume that both the Sylow σ-theorem and τ-theorem hold for G. Then the Sylow π-theorem holds for G. This result confirms a conjecture posed by H. Wielandt in 1959.