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On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups

Published online by Cambridge University Press:  20 November 2018

Francis X. Connolly  and
Stratos Prassidis
Francis X. Connolly
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA, e-mail: [email protected]
Stratos Prassidis
Affiliation:
Department of Mathematics & Statistics, Canisius College, Buffalo, NY 14208, USA, e-mail: [email protected]
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Abstract

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It is known that the $K$-groups that appear in the calculation of 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 $\text{N}{{\text{K}}_{0}}$-groups that appear in the calculation of the ${{K}_{0}}$-groups of virtually infinite cyclic groups.

Keywords

18F2519A31
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 2 , 01 June 2002 , pp. 180 - 195
Copyright
Copyright © Canadian Mathematical Society 2002

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