\(K_{1}\) of a \(p\)-adic group ring. I. The determinantal image. (English) Zbl 1219.19005
Authors’ abstract: We study the K-group K\(_{1}\) of the group ring for a finite group over a coefficient ring which is \(p\)-adically complete and admits a lift of Frobenius. We consider the image of K\(_{1}\) under the determinant map; the central tool is the group logarithm which we can define using the Frobenius lift. Using this we prove a fixed point theorem for the determinantal image of K\(_{1}\).
Reviewer: Sheng Chen (Harbin)
MSC:
| 19B28 | \(K_1\) of group rings and orders |
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