Primitive group rings

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Let K [G] denote the group ring of G over the field K. Until recently it had been an open question as to whether K[G] could be primitive, that is have a faithful irreducible module, if G <1>. An affirmative answer has just been given in the important paper of E. Formanek and R. L. Snider where a large number of examples of primitive group rings were exhibited. In this paper we continue this study.