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Kublanovsky has shown that if a subvariety V of the variety RSn generated by completely 0-simple semigroups over groups of exponent n is itself generated by completely 0-simple semigroups, then it must satisfy one of three conditions: (i) A2 ∈ V; (ii) 
(iii) B2∈V but 
The conditions (i) and (ii) are also sufficient conditions. In this note, we complete Kublanovsky’s programme by refining condition (iii) to obtain a complete set of conditions that are both necessary and sufficient.
