## Journal of the Mathematical Society of Japan

### Cohomology of discrete groups and their finite subgroups

Toshiyuki AKITA

#### Abstract

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 $\mathrm{F}$-isomorphism theorem which remains valid for an arbitrary commutative ring of coefficients and for suitable families of finite subgroups.

#### Article information

Source
J. Math. Soc. Japan, Volume 52, Number 4 (2000), 869-875.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213107114

Digital Object Identifier
doi:10.2969/jmsj/05240869

Mathematical Reviews number (MathSciNet)
MR1774633

Zentralblatt MATH identifier
0982.55010

#### Citation

AKITA, Toshiyuki. Cohomology of discrete groups and their finite subgroups. J. Math. Soc. Japan 52 (2000), no. 4, 869--875. doi:10.2969/jmsj/05240869. https://projecteuclid.org/euclid.jmsj/1213107114