Stable centres of wreath products

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 Gn = Z/p o · · · oZ/p of cyclic groups Z/p is detected by elementary abelian p-subgroups and we describe the resulting coho...

The Wreath Products

Rooted Wreath Products

We introduce “rooted valuation products” and use them to construct universal Abelian lattice-ordered groups (with prescribed set of components) [CHH] from the more classical theory of [Ha]. The Wreath product construction of [H] and [HMc] generalised the Abelian (lattice-ordered) group ideas to a permutation group setting to respectively give universals for transitive (`-) permutation groups wi...

Eigenvalues of Random Wreath Products

Steven N. Evans Department of Statistics #3860, University of California at Berkeley 367 Evans Hall, Berkeley, CA 94720-3860, U.S.A [email protected] Abstract Consider a uniformly chosen element Xn of the n-fold wreath product Γn = G o G o · · · o G, where G is a finite permutation group acting transitively on some set of size s. The eigenvalues of Xn in the natural sn-dimensional permuta...

Wreath Products of Permutation Classes

A permutation class which is closed under pattern involvement may be described in terms of its basis. The wreath product construction X o Y of two permutation classes X and Y is also closed, and we investigate classes Y with the property that, for any finitely based class X, the wreath product X o Y is also finitely based.