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A Characterization of Abelian Groups

L. Brailovsky
Proceedings of the American Mathematical Society
Vol. 117, No. 3 (Mar., 1993), pp. 627-629
DOI: 10.2307/2159119
Stable URL: http://www.jstor.org/stable/2159119
Page Count: 3
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A Characterization of Abelian Groups
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Abstract

Let G be a group and let $k > 2$ be an integer such that $(k^3 - k) < |G|/2$ if G is finite. Suppose that the condition |A2| ≤ k(k + 1)/2 is satisfied by every k-element subset $A \subseteq G$. Then G is abelian.

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