On the Cohomology of Coxeter Groups and Their Finite Parabolic Subgroups Ii
نویسندگان
چکیده
In this paper, we study the relation between the cohomology of Coxeter groups and their parabolic subgroups of nite order. Let W be a Coxeter group and k a commutative ring with identity. We investigate the natural map : H (W; k) ! lim:inv: H (W F ; k), where W F runs all parabolic subgroups of nite order, and prove that the kernel and the cokernel of consist of nilpotent elements. This generalizes our earlier work. The similar result is proved for the Farrell-Tate cohomology. In addition, detections by nite subgroups are also studied in terms of the family of parabolic subgroups of nite order.
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