Locally Finite Simple Groups Whose Nonnilpotent Subgroups Are Pronormal

A subgroup H of a group G is said to be pronormal in G if each of its conjugates Hᵍ in G is already conjugate to it in the subgroup H,Hᵍ . The aim of this paper is to classify those (locally) finite simple groups which have only nilpotent or pronormal subgroups.