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.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 347–360, September, 1969.     

Local definitions of formations of finite groups

A problem of constructing local definitions for formations of finite groups is discussed in the article. The author analyzes relations between local definitions of various types. A new proof of the existence of an ??-composition satellite of an ??-solubly saturated formation is obtained. It is proved that if a nonempty formation of finite groups is $ \mathfrak{X} $ -local by F?rster, then it has an $ \mathfrak{X} $ -composition satellite.