Two Conditions for Infinite Groups to Satisfy Certain Laws

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Let G be an infinite group and . In this paper, we prove that G satisfies the law if and only if in any two infinite subsets X and Y of G, there exist and such that . We also prove that G satisfies the law if and only if in any n infinite subsets , there exist such that .

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Communicated by B.H. Neumann

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Boukaroura , A. Two Conditions for Infinite Groups to Satisfy Certain Laws . Algebra Colloquium 10, 75 –80 (2003). https://doi.org/10.1007/s100110300009

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  • 20F99
  • infinite subsets, variety of groups, commutators