Abstract
Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups (see Theorem 11). Moreover, we show that the stable cohomology of the n-fold wreath product \(G_{n} = \mathbb{Z}/p \wr \ldots \wr \mathbb{Z}/p\) of cyclic groups \(\mathbb{Z}/p\) is detected by elementary abelian p-subgroups and we describe the resulting cohomology algebra explicitly. Some applications to the computation of unramified and stable cohomology of finite groups of Lie type are given.
Mathematics Subject Classification codes (2000): 14E08, 14F43
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Acknowledgements
The first author was supported by NSF grant DMS-1001662 and by AG Laboratory GU- HSE grant RF government ag. 11 11.G34.31.0023. The second author was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft) through Heisenberg-Stipendium BO 3699/1-1.
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Bogomolov, F., Böhning, C. (2013). Isoclinism and Stable Cohomology of Wreath Products. In: Bogomolov, F., Hassett, B., Tschinkel, Y. (eds) Birational Geometry, Rational Curves, and Arithmetic. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6482-2_3
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DOI: https://doi.org/10.1007/978-1-4614-6482-2_3
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