Equivalency of the conjugateness for the X-maximal and X-submaximal subgroups
摘要: Let X be a class of finite groups closed under taking the subgroups, the homomorphic images and the extensions. Denote by D(X) the class of finite groups G such that every two X-maximal subgroups are conjugate in G. In his lectures in 1963, H.Wielandt ask: Are conjugate every two so called X-submaximal subgroups of G if G belongs to D(X)? Equivalently, is D(X) closed under taking the extensions? In the talk, we discuss a solution in the affirmative of this problem and some consequences.