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On the Exponent of the ${\nk}_0$-Groups of Virtually Infinite Cyclic Groups

  Published:2002-06-01
 Printed: Jun 2002
  • Francis X. Connolly
  • Stratos Prassidis
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Abstract

It is known that the $K$-theory of a large class of groups can be computed from the $K$-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the $K$-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of ${\nk}_0$-groups that appear in the calculation of the $K_0$-groups of virtually infinite cyclic groups.
MSC Classifications: 18F25, 19A31 show english descriptions Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
$K_0$ of group rings and orders
18F25 - Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
19A31 - $K_0$ of group rings and orders
 

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