On the exponent of the cokernel of the forget-control map on ${\rm K}_0$-groups
Volume 172 / 2002
Fundamenta Mathematicae 172 (2002), 201-216
MSC: 57N15, 19A31, 19J05, 19M05.
DOI: 10.4064/fm172-3-1
Abstract
For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control ${\rm K}_0$-groups is composed by the ${{\rm NK}}_0$-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.