Mario Curzio,
                                
                                Patrizia Longobardi,
                                
                                Mercede Maj  
                                   (1983)   
                
                
                    Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
                
                
                        
                            
            Let  be a group and  an integer . We say that  has the -permutation property  if, for any elements  in , there exists some permutation  of ,  such that .  We prouve that every group  is an FC-nilpotent group of class , and that a finitely generated group has the -permutation property (for some ) if, and only if, it is abelian by finite. We prouve also that a group  if, and only if, its derived subgroup has order at most 2.