A Characterization of the Gaschütz Subgroup of a Finite Soluble Group

Resumo

Let H be an \( \mathfrak{N} \)-prefrattini subgroup of a soluble finite group G and Δ(G) be its Gaschütz subgroup. In this paper, it is proved that there exist elements x, y ∈ G such that the equality H∩H^x∩H^y = Δ(G) holds.