Locally finite simple groups whose non-Abelian subgroups are pronormal

A subgroup X of a group G is said to be pronormal if the subgroups X and (Formula presented.) are conjugate in (Formula presented.) for all (Formula presented.). Moreover, in analogy with metahamiltonian groups (i.e. groups in which every non-abelian subgroup is normal), a group in which every non-abelian subgroup is pronormal is called prohamiltonian. In this article we will determine those finite simple groups which are prohamiltonian. It will easily follow that the only prohamiltonian locally finite simple groups are the finite ones.