Abstract: 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.
