On the theory of finite groups

This is the author's abstract of his dissertation in the competition for the academic degree of Doctor in the Physico-Mathematical Sciences. The dissertation was defended on the 21st of January, 1969 at the Academic Council of the Institute of Mathematics of the Academy of Sciences of the USSR. The official opponents were: S. N. Chernikov, Corresponding Member, Academy of Sciences of the USSR and Professor B. I. Plotkin, Doctor of Physico-Mathematical Sciences.