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This survey contains results obtained in this area from the second half of the sixties to the present time. In the group of units of the group ring, normal periodic subgroups, elements of finite order, free subgroups, congruence subgroups, questions of conjugacy of finite subgroups, and matrix representations are considered. Moreover, questions connected with the calculation of the groups K0, K I for group rings are discussed with a description of the structure of projective modules, groups of invertib!e matrices, etc.

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In this paper we investigate extended modules for a special class of Ore extensions. We will assume that R is a ring and A will denote the Ore extension A := R[x1, . . . , xn; σ] for which σ is an automorphism of R, xixj = xjxi and xir = σ(r)xi, for every 1 ≤ i, j ≤ n. With some extra conditions over the ring R, we will prove Vaserstein's, Quillen's patching, Horrocks' and Quillen-Suslin's theorems for this type of non-commutative rings.