A permutability problem in infinite groups and Ramsey's theorem

Author:

Abdollahi Alireza,Hassanabadi Aliakbar Mohammadi

Abstract

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 X1XnXσ(1)xσ(n) ≠ θ for some non-identity permutation σ on the set {1,…,n}.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference14 articles.

1. A permutational property of groups

2. [3] Abdoilahi A. , Hassanabadi A. Mohammadi and Taeri B. , ‘An n-rewritability criterion for infinite groups’, Comm. Algebra (to appear).

3. Groups with many rewritable products

4. Fundamentals of the Theory of Groups

5. Sidon Sets in Groups and Induced Subgraphs of Cayley Graphs

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1. On Commutativity and Centrality in Infinite Rings;Communications in Algebra;2007-04-13

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