Journal of the Mathematical Society of Japan

Cohomology of discrete groups and their finite subgroups

Toshiyuki AKITA

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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 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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107114

Digital Object Identifier
doi:10.2969/jmsj/05240869

Mathematical Reviews number (MathSciNet)
MR1774633

Zentralblatt MATH identifier
0982.55010

Subjects
Primary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
Secondary: 20J05: Homological methods in group theory 55R35: Classifying spaces of groups and $H$-spaces

Keywords
Group cohomology Farrell-Tate cohomology discrete group

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


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