We prove that if p is a prime and W is the standard wreath product of two nontrivial cyclic p-groups X and Y then W is isomorphic to the full automorphism group of some group if and only if |X| = 2 and |Y | is 2 or 4.

We give a formula for the character of the representation of the Weyl group Sn on each isotypic component of the cohomology of the set of regular elements of a maximal torus of SLn, with respect to the action of the centre. As a consequence, we find that this representation is induced from a cohomology representation of a wreath product subgroup.

the reciprocal degree distance (rdd)‎, ‎defined for a connected graph $g$ as vertex-degree-weighted sum of the reciprocal distances‎, ‎that is‎, ‎$rdd(g) =sumlimits_{u,vin v(g)}frac{d_g(u)‎ + ‎d_g(v)}{d_g(u,v)}.$ the reciprocal degree distance is a weight version of the harary index‎, ‎just as the degree distance is a weight version of the wiener index‎. ‎in this paper‎, ‎we present exact formu...

Given two finite p-local finite groups and a fusion preserving morphism between their Sylow subgroups, we study the question of extending it to a continuous map between the classifying spaces. The results depend on the construction of the wreath product of p-local finite groups which is also used to study p-local permutation representations.

We prove analogues for sub-posets of the Dowling lattices of the results of Calderbank, Hanlon, and Robinson on homology of sub-posets of the partition lattices. The technical tool used is the wreath product analogue of the tensor species of Joyal.

We give a positive answer, in the measurable-group-theory context, to von Neumann’s problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group von Neumann factor into restricted wreath product factors. 2000 Mathematical Subject Classification: 37A20, 20E05, 82B43, 05C80

Let A be a compact quantum group, let n ∈ N∗ and let Aaut(Xn) be the quantum permutation group on n letters. A free wreath product construction A∗wAaut(Xn) is done. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.

In this paper, we compute an upper bound for the Dehn function of a finitely presented metabelian group. addition, prove that same works relative generated We also show every wreath product free abelian group finite rank with can be embedded into exponential function.

We study representations of wreath product analogues of categories of finite sets. This includes the category of finite sets and injections (studied by Church, Ellenberg, and Farb) and the opposite of the category of finite sets and surjections (studied by the authors in previous work). We prove noetherian properties for the injective version when the group in question is polycyclic-by-finite a...

We give a simple and unified proof showing that the unrestricted wreath product of weakly sofic, linear or hyperlinear group by an amenable is hyperlinear, respectively. By means Kaloujnine-Krasner theorem, this implies extensions with quotients preserve four aforementioned metric approximation properties. also discuss case co-amenable groups.