Product graphs for given subgroups of the wreath product of two groups, I

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...

Primitive Subgroups of Wreath Products in Product Action

This paper is concerned with finite primitive permutation groups G which are subgroups of wreath products W in product action and are such that the socles of G and W are the same. The aim is to explore how the study of such groups may be reduced to the study of smaller groups. The O'Nan-Scott Theorem (see Liebeck, Praeger, Saxl [12] for the most recent and detailed treatment) sorts finite primi...

Image Processing with Wreath Product Groups

Finitely Presented Subgroups of a Product of Two Free Groups

We use van Kampen diagram techniques to give a new geometric proof of Baumslag and Roseblade’s result that a non–free finitely presented subgroup of a direct product of two free groups is virtually a product of subgroups of the factors.