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Math. Z. 228, 229–246 (1998) c Springer-Verlag 1998 1;? 2 Manfred Kolster , Reinhard C. Laubenbacher Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada (e-mail: kolster@mcmaster.ca) Department of Mathematics, New Mexico State University, Las Cruces, NM 88003, USA (e-mail: reinhard@nmsu.edu) Received 10 May 1995; in final form 3 September 1996 Introduction One of the high points in the study of the K -theory of group rings and orders was R. Oliver’s investigation of SK (Z[G]) for finite groups G, in a series of deep papers, summarized in [Ol]. He defined the higher class group Cl (Z[G]) = ker SK (Z[G]) −! SK (Z [G]) ; 1 1 1 p which measures the obstruction to a local-global principle for SK (Z[G]). In many cases all the local groups vanish. Some of Oliver’s principal tools were conductor squares and the Moore sequence. In this paper we use arithmetic squares and higher dimensional analogues of the Moore sequence to study the odd dimensional class groups Cl (), 2n−1 n 1,ofan O -order in a semi-simple algebra over a number field F with ring of integers O . These are defined as Cl ()= ker SK () −! SK
Mathematische Zeitschrift – Springer Journals
Published: Jun 1, 1998
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