“School of Mathematics”
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| Paper IPM / M / 527 |
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| Abstract: | |
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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 X1…Xn∩Xσ(1) …Xσ(n) ≠ ∅ for some non-identity
permutation σ on the set {1,…, n}.
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