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Paper   IPM / M / 527
School of Mathematics
  Title:   A permutability problem in infinite groups and Ramsey's theorem
  Author(s):  A. Abdollahi (joint with A. Mohammadi Hassanabadi)
  Status:   Published
  Journal: Bull. Aust. Math. Soc.
  Vol.:  64
  Year:  2001
  Pages:   27-31
  Supported by:  IPM
  Abstract:
We use Ramsey's theorem to generalise a result of L. Babai and T.S. Sos on Sidon subsets and then use this to prove that for an integer n > 1 the class of groups in which every infinite subset contains a rewritable n-subset coincides with the class of groups in which every infinite subset contains n mutually disjoint non-empty X1,…, Xn such that X1XnXσ(1)Xσ(n) ≠ ∅ for some non-identity permutation σ on the set {1,…, n}.

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