Separability and efficiency under standard wreath product in terms of Cayley graphs

Abstract

In this paper we are mainly interested in separability and efficiency under the standard wreath product. To do that we will first obtain a presentation, say P(G), for the standard wreath product in terms of Cayley graphs. Then we will prove our first main result of this paper, which can be thought of as an application of the result given in [17] (or the general result in [6]). Moreover, by considering the standard wreath product G of any finite groups B by A, we will define the relationship between B-separability and efficiency, on G, as another main result of this paper.