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  • LMS Journal of Computation and Mathematics, Volume 12
  • January 2009, pp. 166-194

Computations in Relative Algebraic K-Groups

  • Werner Bley (a1) and Stephen M. J. Wilson (a2)
  • DOI: http://dx.doi.org/10.1112/S1461157000001480
  • Published online: 01 February 2010
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

9.T. Chinburg , Exact sequences and Galois module structure, Ann. of Math. 121 (1985), 351376.

10.H. Cohen , A course in computational algebraic number theory, Springer Verlag (1993).

11.H. Cohen , Advanced topics in computational number theory, Springer Verlag (2000).

15.T. Nakayama and Y. Matsushima , Über die multiplikative Gruppe einer p-adischen Divisionsalgebra, Proc. Imp. Acad. Tokyo 19 (1943) 622628.

17.R. G. Swan , Algebraic K -theory, Lecture Notes in Mathematics 76, Springer Verlag (1968).

18.S. Wang , On the commutator group of a simple algebra, Amer. J. Math. 72 (1950) 323334.

19.M. J. Taylor , On Fröhlich's conjecture for rings of integers of tame extensions, Inventiones Mathematicae, 63 (1981), 4179.

20.André Weil , Basic Number Theory, Springer-Verlag (1974).

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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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