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Computations in Relative Algebraic K-Groups

Bley, Werner
Wilson, Stephen M. J.

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Classification / Keywords
Citation
In: Mathematische Schriften Kassel 07, 08 / (2007) , S. ; 
@article{urn:nbn:de:hebis:34-2008022920579,
  author    ={Bley, Werner and Wilson, Stephen M. J.},
  title    ={Computations in Relative Algebraic K-Groups},
  copyright  ={https://rightsstatements.org/page/InC/1.0/},
  language ={en},
  year   ={2007}
}