Maximal prime homomorphic images of mod-p Iwasawa algebras

Let k be a finite field of characteristic p, and G a compact p-adic analytic group. Write kG for the completed group ring of G over k. In this paper, we describe the structure of the ring kG/P, where P is a minimal prime ideal of kG. We give an explicit isomorphism between kG/P and a matrix ring with coefficients in the ring, where is a finite field extension, is a large subquotient of G with no finite normal subgroups, and (-) α is a twisting operation that preserves many desirable properties of the ring structure. We demonstrate the usefulness of this isomorphism by studying the correspondence induced between certain ideals of kG and those of, and showing that this preserves many useful group-theoretic properties of ideals, in particular almost-faithfulness and control by a closed normal subgroup.