On the Small Squaring and Commutativity |
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| Authors: | Brailovsky L |
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| Institution: | School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University Ramat-Aviv, 69978 Israel |
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| Abstract: | Let G be a group and let k > 2 be an integer, such that (k2– 3)(k – 1) < |G|/15 if G is finite. Supposethat the condition |A2|  k(k + 1)/2 + (k – 3)/2 is satisfiedby every it-element subset A  G. Then G is abelian. The proofuses the structure of quasi-invariant sets. |
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