Abstract
We characterize orthogroups, local orthogroups and (left,right) cryptogroups within completely regular semigroups by means of absence of certain kind of subsemigroups. For each of these varieties V, we determine the complete set of minimal non-V -varieties. For each of the latter varieties, we determine the lattice of its subvarieties. We then give a generating semigroup and a basis of its identities for every variety which occurs in this way. The subvariety lattices are illustrated by three diagrams.
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