a1 Fachbereich für Mathematik der Universität Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany, firstname.lastname@example.org
a2 Heilbronn Institute for Mathematical Research, University Of Bristol, Royal Fort Annexe, Clifton, Bristol BS8 1TW, United Kingdom, email@example.com
Let G be finite group and K a number field or a p-adic field with ring of integers OK. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K0(OK[G], K) as an abstract abelian group. We also give algorithms to solve the discrete logarithm problems in K0(OK[G], K) and in the locally free class group cl(OK[G]). All algorithms have been implemented in Magma for the case K = Q.
In the second part of the manuscript we prove formulae for the torsion subgroup of K0(Z[G], Q) for large classes of dihedral and quaternion groups.
(Received February 28 2008)
(Revised March 17 2009)