Abstract
If a group G of finite virtual cohomological dimension has p-periodic Farrell cohomology, then the Yagita invariant of this group equals its p-period. The group of symplectic 2(p + 1) × 2(p + 1) matrices over \({\mathbb{Z}}\) has elementary abelian p-subgroups of rank at least 2 and hence \({{\rm Sp}(2(p+1), \mathbb{Z})}\) and \({{\rm Sp}(2(p+1), \mathbb{Q})}\) do not have p-periodic Farrell cohomology. We compute the Yagita invariants of these groups for any odd prime p.
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This article is a publication of results of the habilitation thesis [4] of the author.
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Busch, C.M. The Yagita Invariant of Some Symplectic Groups. Mediterr. J. Math. 10, 137–146 (2013). https://doi.org/10.1007/s00009-011-0166-0
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DOI: https://doi.org/10.1007/s00009-011-0166-0