Petechuk I. Homomorphisms of the matrix groups over associative rings.

The dissertation is devoted to the study of homomorphisms of the matrix groups over associative rings with 1.It is proved that homomorphisms with the condition (*) of the matrix groups , in the group of automorphisms of the left (not necessarily free) -module over arbitrary associative rings and with 1 have the standard description in the group of elementary transvections .The application of homomorphisms with the condition (*) to the description of isomorphisms of the matrix groups over commutative rings is shown without the use of the description of the normal structure of the matrix groups.A description of homomorphisms with the condition (*) of subgroups of complete linear groups over associative rings with 1, in which the subgroups of elementary transvections are normal, is obtained.