Isoclinism and stable cohomology of wreath products
  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. 
Fedor Bogomolov, Christian B\"ohning
math.AG