Isoclinism and Stable Cohomology of Wreath Products

Ch. 3. 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.

Ключевые слова: алгебраическая геометрия, algebraic geometry

В книге

Birational geometry, rational curves, and arithmetic

Boston: Birkhäuser, 2013.