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.

We describe the upper and lower Lie nilpotency index of a modular group algebra ‫ކ‬G of some metabelian group G and apply these results to determine the nilpotency class of the group of units, extending certain results of Shalev without restriction to finite groups. A characterization of modular group algebras ‫ކ‬G with group of units of class 3 is given, which was obtained by Rao and Sandling for finite groups G. ᮊ

No abstract

No abstract

No abstract