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. [ABSTRACT FROM AUTHOR]