On extensions of completely simple semigroups by groups

Abstract

An example of an extension of a completely simple semigroup $$U$$ by a group $$H$$ is given which cannot be embedded into the wreath product of $$U$$ by $$H$$ . On the other hand, every central extension of $$U$$ by $$H$$ is shown to be embeddable in the wreath product of $$U$$ by $$H$$ , and any extension of $$U$$ by $$H$$ is proved to be embeddable in a semidirect product of a completely simple semigroup $$V$$ by $$H$$ where the maximal subgroups of $$V$$ are direct powers of those of $$U$$ .