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Isoclinism and Stable Cohomology of Wreath Products

P. 57-76.
Fedor Bogomolov, Böhning C.

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.

В книге

Под науч. редакцией: F. A. Bogomolov, B. Hasset, Y. Tschinkel. Boston: Birkhäuser, 2013.