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Proceedings of the American Mathematical Society

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A characterization of abelian groups


Author: L. Brailovsky
Journal: Proc. Amer. Math. Soc. 117 (1993), 627-629
MSC: Primary 20A05; Secondary 20K99
DOI: https://doi.org/10.1090/S0002-9939-1993-1129873-0
MathSciNet review: 1129873
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Abstract: Let $ G$ be a group and let $ k > 2$ be an integer such that $ ({k^3} - k) < \vert G\vert/2$ if $ G$ is finite. Suppose that the condition $ \vert{A^2}\vert \leqslant k(k + 1)/2$ is satisfied by every $ k$-element subset $ A \subseteq G$. Then $ G$ is abelian.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1129873-0
Article copyright: © Copyright 1993 American Mathematical Society

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