K1 of a p  -adic group ring II. The determinantal kernel SK1

T. Chinburg ^[1] ; G. Pappas ^[2] ; M.J. Taylor ^[3]
1. [1] University of Pennsylvania
  
  University of Pennsylvania
  
  City of Philadelphia, Estados Unidos
2. [2] Michigan State University
  
  Michigan State University
  
  City of East Lansing, Estados Unidos
3. [3] Oxford University, United Kingdom
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Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 7 (July 2015), 2015, págs. 2581-2623
Idioma: inglés
DOI: 10.1016/j.jpaa.2014.09.017
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Resumen
- We describe the group SK1(R[G])SK1(R[G]) for group rings R[G]R[G] where G is an arbitrary finite group and where the coefficient ring R is a p-adically complete Noetherian integral domain of characteristic zero which admits a lift of Frobenius and which also satisfies a number of further mild conditions. Our results extend previous work of R. Oliver who obtained such results for the valuation rings of finite extensions of the p-adic field.