Artemovych O. Groups nearly to the indecomposable groups and related ring theory problems.

The dissertation is devoted to investigating of indecomposable and nearly indecomposable groups and related problems of ring theory. We describe properties of non-perfect groups without a proper factorization. It is obtained the solutions of two problems of F.Szasz and we prove (by mod CFSG) an analogues of Glauberman Z*-theorem for old primes. A construction of Frobenius groups which is associated with a module over a right primitive ring is presented. We presente also the construction of a group H(I,T) which is associated with a pair (I,T), where I is a non-trivial submodule of a left R-module M, T a non-trivial subgroup of the adjoint group R( of an associative ring R. We find a criteria for H(I,T) to be a Frobenius group and obtain some results on the Jacobson radical rings and he groups related to the Charin groups. We investigate properties of HM*-groups and, in particular, the minimal non-''hypercentral-by-finite" groups. For the constructions of examples of HM*-groups we characterize the d ifferentially trivial and respectively rigid rings. The differentially trivial domains and the differentially trivial left Noetherian rings also are described. We find a criteria when every extension of an abelian group A by an abelian operator group B is nilpotent and respectively hypercentral, or Engel. The solvable groups with the minimal condition on non-hypercentral (respectively non-nilpotent, non-''nilpotent-by-finite", on non-''hypercentral-by-finite") subgroups are described. We characterize the torsion locally nilpotent groups with the maximal condition on non-nilpotent (respectively non-hypercentral) subgroups and the solvable groups with many nilpotent-by-Chernikov subgroups.