A characterization of abelian groups

Author:

Brailovsky L.

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference4 articles.

1. Small squaring and cubing properties for finite groups;Berkovich, Ya. G.;Bull. Austral. Math. Soc.,1991

2. On two- and three-element subsets of groups;Freĭman, G. A.;Aequationes Math.,1981

3. On a combinatorial problem in group theory;Herzog, Marcel;Israel J. Math.,1993

4. P. Longobardi and M. Maj, The classification of groups with the small squaring property on 3-sets (to appear).

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