For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-3-1, author = {Francis X. Connolly and Stratos Prassidis}, title = {On the exponent of the cokernel of the forget-control map on K0-groups}, journal = {Fundamenta Mathematicae}, volume = {173}, year = {2002}, pages = {201-216}, zbl = {0992.57022}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-3-1} }
Francis X. Connolly; Stratos Prassidis. On the exponent of the cokernel of the forget-control map on K₀-groups. Fundamenta Mathematicae, Tome 173 (2002) pp. 201-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm172-3-1/