Automorphisms, factorizations and theorems of Sylow-type theorems

In this paper finite groups with restrictions on certain subgroups are studied. A generalization of Wielandt's theorem on groups having a nilpotent Hall subgroup is obtained. A conjecture by S. A. Chunikhin on the nonsimplicity of a finite group having two classes of nontrivial elements of odd order with relatively prime centralizer indexes is also confirmed.
Bibliography: 22 titles.