we regard the shearlet group as a semidirect product group andshow that its standard representation is,typically, a quasiregu-lar representation. as a result we can characterize irreducibleas well as square-integrable subrepresentations of the shearletgroup.

In his 1996 work developing the theory of association schemes as a ‘generalized’ group theory, Zieschang introduced the concept of the semidirect product as a possible product operation of certain association schemes. In this paper we extend the semidirect product operation into the entire set of association schemes. We then derive a way to decompose certain association schemes into smaller ass...

In this paper, we prove that the Birget-Rhodes expansion G̃R of a group G is not a semidirect product of a semilattice by a group but it can be nicely embedded into such a semidirect product.

‎we investigate two constructions‎ - ‎the replacement and the zig-zag‎ ‎product of graphs‎ - ‎describing several fascinating connections‎ ‎with combinatorics‎, ‎via the notion of expander graph‎, ‎group‎ ‎theory‎, ‎via the notion of semidirect product and cayley graph‎, ‎and‎ ‎with markov chains‎, ‎via the lamplighter random walk‎. ‎many examples‎ ‎are provided‎.

In this paper, we introduce a new product operation of association schemes in order to generalize the notion of semidirect products and wreath product. We then show that our construction covers some association schemes which are neither wreath products nor semidirect products of two given association schemes.

In this paper we prove two main results. The first is a necessary and sufficient condition for a semidirect product of a semilattice by a group to be finitely generated. The second result is a necessary and sufficient condition for such a semidirect product to be finitely presented. 2000 Mathematics subject classification: primary 20M05; secondary 20M18, 20M30.