Embedding of regular semigroups in wreath products. II (Q1084513)

[Part I see ibid. 29, 177-207 (1983; Zbl 0572.20045.] A semigroup \({\mathcal S}\) is called natural locally \({\mathcal R}\)-unipotent if the union of its maximal subgroups is a sub-semigroup and for each idempotent element \(e\in {\mathcal S}\) the \({\mathcal R}\)-class of e\({\mathcal S}e\) contains exactly one idempotent. The main result of this paper (Theorem 37 of 50 numbered lemmas, remarks, propositions, theorems, and corollaries!) provides an embedding of natural locally \({\mathcal R}\)- unipotent semigroups in wreath products of simpler semigroups.