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- Title
The Cohomology of Pro- p-Groups with Group Ring Coefficients and Virtual Poincare Duality.
- Authors
Korenev, A. A.
- Abstract
The relationship between the group-theoretic properties of a pro- p-group G and the G-module structure of the group $$H^n (G,\mathbb{F}_q \left[\kern-0.15em\left[ G \right]\kern-0.15em\right])$$ is studied. A necessary and sufficient condition for a pro- p-group G to contain an open Poincare subgroup of dimension n is obtained. This condition does not require that G have finite cohomological dimension and, therefore, applies to groups with torsion. Results concerning the possible values of $$\dim _{\mathbb{F}p} H^n (G,\mathbb{F}_p \left[\kern-0.15em\left[ G \right]\kern-0.15em\right])$$ are also obtained.
- Subjects
POINCARE series; DUALITY (Logic); GROUP theory; GROUP rings; TORSION
- Publication
Mathematical Notes, 2005, Vol 78, Issue 5/6, p791
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0184-y