Let { cal N}_c be the variety of nilpotent groups of class at most c (c geq 2) and G=Z_r oplus Z_s be the direct sum of two finite cyclic groups. It is shown that if the greatest common divisor of r and s is not one, then G does not have any { cal N}_c -covering group for every c geq 2 . This result gives an idea that Lemma 2 of J.Wiegold [6] and Haebich s Theorem [1], a vast generalization of the Wiegold s Theorem, can { it not} be generalized to the variety of nilpotent groups of class at most c geq 2 .

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