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A characterization of infinite 3-abelian groups |
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| Authors: | Alireza Abdollahi |
| Institution: | Department of Mathematics, University of Isfahan, Isfahan, Iran, IR |
| Abstract: | In this note we prove that every infinite group G is 3-abelian (i.e. (ab)3 = a3b3 for all a, b in G) if and only if in every two infinite subsets X and Y of G there exist x ? Xx\in X and y ? Yy\in Y such that (xy)3 = x3y3. |
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