COVERS FOR REGULAR-SEMIGROUPS AND AN APPLICATION TO COMPLEXITY

A major result of D.B. McAlister for inverse semigroups is generalised in the paper to classes of regular semigroups, including the class of all regular semigroups. It is shown that any regular semigroup is a h omomorphic image of a regular semigroup whose least full self-conjugat e subsemigroup is unitary; the homomorphism is injective on the subsem igroup. As an application, the group complexity of any finite E-solid regular semigroup is shown to be the same as, or one more than that of its least full self-conjugate subsemigroup (the subsemigroup is compl etely regular and is the type II subsemigroup). In an addition to the paper, by P.R. Jones, it is shown that any finite locally orthodox sem igroup has group complexity 0 or 1.