The work is devoted to the investigation of sharply Jc-transitive sets of permutations which are a natural generalization of sharply k-transitive groups. Its main result is the establishment of the connection between such notions as sharply Jc-transitive sets of permutations, sharply fc-transitive loops of permutations (introduced by F.Bonetti, GXunardon and K.Strambach) and loop transversals.