A Characterization of Abelian Groups
Copyright policy )A Characterization of Abelian Groups
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.
Generators, relations, and presentations of groups, General structure theorems for groups, small squaring property, finite by elementary abelian, abelian by finite, Arithmetic and combinatorial problems involving abstract finite groups
Generators, relations, and presentations of groups, General structure theorems for groups, small squaring property, finite by elementary abelian, abelian by finite, Arithmetic and combinatorial problems involving abstract finite groups
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