Preprint
Computations in Relative Algebraic K-Groups
Zusammenfassung
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.
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@article{urn:nbn:de:hebis:34-2008022920579,
author={Bley, Werner and Wilson, Stephen M. J.},
title={Computations in Relative Algebraic K-Groups},
year={2007}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2007$n2007 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008022920579 3000 Bley, Werner 3010 Wilson, Stephen M. J. 4000 Computations in Relative Algebraic K-Groups / Bley, Werner 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008022920579=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 07, 08 7136 ##0##urn:nbn:de:hebis:34-2008022920579
2008-02-29T09:38:19Z 2008-02-29T09:38:19Z 2007 urn:nbn:de:hebis:34-2008022920579 http://hdl.handle.net/123456789/2008022920579 366580 bytes 155155 bytes application/pdf application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Relative algebraic K-groups of integral group rings 510 Computations in Relative Algebraic K-Groups Preprint 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. open access Bley, Werner Wilson, Stephen M. J. Mathematische Schriften Kassel ;; 07, 08 19A99 19F99 19B28 Mathematische Schriften Kassel 07, 08
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