On the Bergman Property for the Automorphism Groups of Relatively Free Groups |
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Authors: | Tolstykh Vladimir |
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Affiliation: | Department of Mathematics, Yeditepe University 34755 Kayda, Istanbul, Turkey vtolstykh{at}yeditepe.edu.tr |
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Abstract: | A group G is said to have the Bergman property (the propertyof uniformity of finite width) if given any generating X withX = X1 of G, we have that G = Xk for some natural k,that is, every element of G is a product of at most k elementsof X. We prove that the automorphism group Aut(N) of any infinitelygenerated free nilpotent group N has the Bergman property. Also,we obtain a partial answer to a question posed by Bergman byestablishing that the automorphism group of a free group ofcountably infinite rank is a group of uniformly finite width. |
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