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/