The indecomposability of certain wreath products indexed by partially ordered sets (Q788832)

In this paper the authors continue their work on wreath products of groups indexed by partially ordered sets. The paper is concerned with the question of when such a wreath product decomposes as a direct product of two non-trivial groups. The authors give necessary and sufficient conditions for a wreath product to decompose, therefore generalizing a result of \textit{P. M. Neumann} [Math. Z. 84, 343-373 (1964; Zbl 0122.029)]. Several examples are given to illustrate the main theorem.