Abstract
AbstractRecently, Baumslag and Wiegold proved that a finite group G is nilpotent if and only if for every of coprime order. Motivated by this result, we study the groups with the property that and those with the property that for every and every nontrivial of pairwise coprime order. We also consider several ways of weakening the hypothesis on x and y. While the result of Baumslag and Wiegold is completely elementary, some of our arguments here depend on (parts of) the classification of finite simple groups.
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