On the Characterization of the Core of a π-Prefrattini Subgroup of a Finite Soluble Group

Resumo

Let π be a set of primes and let H be a π-prefrattini subgroup of a finite soluble group G. We prove that there exist elements x, y, z ∈ G such that H ∩ H^x ∩ H^y ∩ H^z = Φ_π(G).