On Subsets with Small Product in Torsion-Free Groups


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 .

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Received: October 13, 1997/Revised: Revised August 18, 1998

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Hamidoune, Y., Lladó, A. & Serra, O. On Subsets with Small Product in Torsion-Free Groups. Combinatorica 18, 529–540 (1998). https://doi.org/10.1007/s004930050038

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  • AMS Subject Classification (1991) Classes:  20D60, 11B75