ON KUROSH-AMITSUR RADICALS OF FINITE GROUPS

Between 1952 and 1954 Amitsur and Kurosh initiated the general theory of radicals in various contexts. In the case of all groups some interesting results concerning radicals were obtained by Kurosh, Shchukin, Ryabukhin, Gardner and others. In this paper we are going to examine radical theory in the class of all nite groups. This strong restriction gives chance to obtain stronger results, then in the case of all groups. For example, we obtain a complete description of hereditary and of strongly hereditary radicals in the class of all nite groups.