Abstract
In a recent preprint, George M. Bergman has investigated the following property: for any generating set X of the group G there exists an integer n such that any element of G is a product of n elements of X ∪ X −1 . We will say in this case that G has the Bergman property. We have solved some of the questions asked in the above mentioned preprint and have found it suitable to investigate this property in a more general context, in particular for rings (essentially Boolean rings). To cite this article: A. Khelif, C. R. Acad. Sci. Paris, Ser. I 342 (2006).
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