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 Gn=Z/p…Z/p of cyclic groups 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.
|Original language||English (US)|
|Title of host publication||Birational Geometry, Rational Curves, and Arithmetic|
|Publisher||Springer New York|
|Number of pages||20|
|State||Published - Jan 1 2013|
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