On Subsets with Small Product in Torsion-Free Groups |
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| Authors: | Y. O. Hamidoune A. S. Lladó O. Serra |
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| Affiliation: | (1) CNRS; Paris, France; E-mail: yha@ccr.jussieu.fr, FR;(2) Universitat Politècnica de Catalunya; Barcelona, Spain; E-mail: anna@mat.upc.es, ES;(3) Universitat Politècnica de Catalunya; Barcelona, Spain; E-mail: oriol@mat.upc.es, ES |
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| Abstract: | G be a nonabelian torsion-free group. Let C be a finite generating subset of G such that . We prove that, for all subsets B of G with , we have . In particular, a finite subset X with cardinality satisfies the inequality if and only if there are elements , such that the following two conditions hold: (i) . (ii) where . Received: October 13, 1997/Revised: Revised August 18, 1998 |
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| Keywords: | AMS Subject Classification (1991) Classes: 20D60, 11B75 |
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