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A permutability problem in infinite groups and Ramsey's theorem

Published online by Cambridge University Press:  17 April 2009

Alireza Abdollahi  and
Aliakbar Mohammadi Hassanabadi
Alireza Abdollahi
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81744, Iran and Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran e-mail: abdolahi@math.ui.ac.iraamohaha@math.ui.ac.ir
Aliakbar Mohammadi Hassanabadi
Affiliation:
Department of Mathematics, University of Isfahan, Isfahan 81744, Iran and Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran e-mail: abdolahi@math.ui.ac.iraamohaha@math.ui.ac.ir
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Abstract

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We use Ramsey's theorem to generalise a result of L. Babai and T.S. Sós 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 ever infinite subset contains n mutually disjoint non-empty subsets X1,…,Xn such that X1…Xn∩Xσ(1) …xσ(n) ≠ θ for some non-identity permutation σ on the set {1,…,n}.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 27 - 31
Copyright
Copyright © Australian Mathematical Society 2001

References

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