A problem on central cryptogroups.
A completely regular semigroup \(S\) is called `central' if the product of any two idempotents of \(S\) lies in the center of the maximal subgroup containing it; if the Green relation \(\mathcal H\) is a congruence on \(S\), then \(S\) is called a `cryptogroup'. The classes of all cryptogroups, central cryptogroups and orthodox cryptogroups are denoted by \(\mathcal{BG}\), \(\mathcal{CBG}\) and \(\mathcal{OBG}\), respectively. A completely regular semigroup \(S\) is called `overabelian' if \(H_e\) are Abelian groups for all \(e\in E(S)\). \(\mathcal{BA}\) denotes the class of all overabelian cryptogroups. It is proved that \(\mathcal{OBG}\vee\mathcal{BA}=\mathcal{CBG}\).
scientific article; zbMATH DE number 5118906