Cohomology of discrete groups and their finite subgroups

Dedicated to the memory of Professor Katsuo Kawakubo

抄録

We investigate the cohomology of a group having finite virtual cohomological dimension in terms of the contributions from finite subgroups. As a result, we prove a variant of Quillen's F-isomorphism theorem which remains valid for an arbitrary commutative ring of coefficients and for suitable families of finite subgroups.