Isoclinism and Stable Cohomology of Wreath Products

Fedor Bogomolov () and Christian Böhning ()
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Fedor Bogomolov: Courant Institute of Mathematical Sciences
Christian Böhning: Fachbereich Mathematik der Universität Hamburg

A chapter in Birational Geometry, Rational Curves, and Arithmetic, 2013, pp 57-76 from Springer

Abstract: 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.

Keywords: Stable Cohomology; Iterated Wreath Product; Abelian Subgroup; Finite Group; Algebra Cohomology (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-6482-2_3

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DOI: 10.1007/978-1-4614-6482-2_3

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