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Computations in Relative Algebraic K-Groups

Published online by Cambridge University Press:  01 February 2010

Werner Bley  and
Stephen M. J. Wilson
Werner Bley
Affiliation:
Fachbereich für Mathematik der Universität Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany, [email protected]
Stephen M. J. Wilson
Affiliation:
Heilbronn Institute for Mathematical Research, University Of Bristol, Royal Fort Annexe, Clifton, Bristol BS8 1TW, United Kingdom, [email protected]

Abstract

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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.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 12 , 2009 , pp. 166 - 194
Copyright
Copyright © London Mathematical Society 2009

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