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 ${(k'G')_\alpha }$ , where $k'/k$ is a finite field extension, $G'$ 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 ${(k'G')_\alpha }$ , and showing that this preserves many useful “group-theoretic” properties of ideals, in particular almost-faithfulness and control by a closed normal subgroup.

中文翻译：

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mod-p岩泽代数的最大素数同态图像

让ķ是一个有限的特征域p， 和G紧凑的p-adic 解析群。写公斤对于完成的组环G超过ķ. 在本文中，我们描述了环的结构公斤/磷， 在哪里磷是一个最小素理想公斤. 我们给出了一个明确的同构公斤/磷和一个矩阵环，环中有系数${(k'G')_\alpha }$， 在哪里$k'/k$是有限域扩展，$G'$是一个大的子商G没有有限正规子群，并且 (-)α是一种“扭曲”操作，它保留了环结构的许多理想特性。我们通过研究某些理想之间的对应关系来证明这种同构的有用性公斤和那些${(k'G')_\alpha }$，并表明这保留了理想的许多有用的“群论”特性，特别是近乎忠实和封闭正态子群的控制。