A note on generalised wreath product groups

Image Processing with Wreath Product Groups

Automorphism Groups of Wreath Product Digraphs

We strengthen a classical result of Sabidussi giving a necessary and sufficient condition on two graphs, X and Y , for the automorphsim group of the wreath product of the graphs, Aut(X o Y ) to be the wreath product of the automorphism groups Aut(X) o Aut(Y ). We also generalize this to arrive at a similar condition on color digraphs. The main purpose of this paper is to revisit a well-known an...

Automorphisms of Regular Wreath Product p-Groups

We present a useful new characterization of the automorphisms of the regular wreath product group P of a finite cyclic p-group by a finite cyclic p-group, for any prime p, and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut P , where P is the regular wreath product of a finite cyclic p-group by...

On a pattern avoidance condition for the wreath product of cyclic groups with symmetric groups

In this paper, we extend, to a non-consecutive case, the study of the pattern matching condition on the wreath product Ck o Sn of the cyclic group Ck and the symmetric group Sn initiated in [2]. The main focus of our paper is (colored) patterns of length 2, although a number of enumerative results for longer patterns are also presented. A new non-trivial bijective interpretation for the Catalan...

Conjugacy growth series for wreath product finitary symmetric groups

In recent work, Bacher and de la Harpe define and study conjugacy growth series for finitary permutation groups. In two subsequent papers, Cotron, Dicks, and Fleming study the congruence properties of some of these series. We define a new family of conjugacy growth series for the finitary alternating wreath product that are related to sums of modular forms of integer and half-integral weights, ...