Isoclinism and stable cohomology of wreath products

Details Isoclinism and stable cohomology of wreath products Isoclinism and stable cohomology of wreath products

2012-04-20

arxiv.org/abs/1204.4747v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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 4.4. Moreover, we show that the stable cohomology of the n-fold wreath product of cyclic groups ZZ/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.

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