Computations in Relative Algebraic K-groups
نویسندگان
چکیده
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 solve the discrete logarithm problem, both in K0(OK [G], K) and 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.
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تاریخ انتشار 2007