Theorems of Sylow type

Let  be a set of primes. Generalizing the known properties of Sylow subgroups, Hall introduced the classes , , and  of finite groups that contain a Hall -subgroup, precisely one conjugacy class of Hall -subgroups, and precisely one conjugacy class of maximal -subgroups, respectively. The present paper concerns results about , , and  that have been obtained by different authors at different times. Bibliography: 113 titles.