The p-cockcroft property of the semi-direct products of monoids

Abstract

The semi-direct product of arbitrary two monoids and a presentation for this product have received considerable attention, see for instance [12, 14, 15]. In [15], Wang defined a trivializer set of the Squier complex associated with this presentation. In this paper, as a main result, we discuss necessary and sufficient conditions for the standard presentation of the semi-direct product of any two monoids to be p-Cockcroft for any prime p or 0. Finally we present some applications of this main theorem