On groups with a finite number of automorphisms

It is proved that in groups having only a finite number of automorphisms the set of all prime numbers dividing the finite orders of elements is finite. The dependence of the order of a finite group on the number of its automorphisms is obtained. A new proof is given of the well-known result of Baer that a periodic group with a finite number of automorphisms is finite. It is proved that a group with a finite number of monomorphisms is finite. The final result generalizes the well-known theorem of Baer that a group with a finite number of endomorphisms is finite.
Bibliography: 5 titles.