Five degrees of separation
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- by Péter Komjáth PDF
- Proc. Amer. Math. Soc. 130 (2002), 2413-2417 Request permission
Abstract:
If $A$ is an infinite Abelian group, $S\subseteq A \times A$, then $S$ can be transformed in five steps of type $(x,y)\mapsto (x,y+f(x))$ or $(x,y)\mapsto (x+f(y),y)$ into a predetermined subset of the diagonal (depending on $\min (|S|,|(A\times A)-S|)$).References
- M. Abért: Every infinite symmetric group is the product of finitely many Abelian groups, to appear.
- M. Abért, T. Keleti: Shuffle the plane, Proc. Amer. Math. Soc. 130 (2002), 549–553. .
Additional Information
- Péter Komjáth
- Affiliation: Department of Computer Science, Eötvös University, Budapest, P.O. Box 120, 1518, Hungary
- MR Author ID: 104465
- Email: kope@cs.elte.hu
- Received by editor(s): November 29, 2000
- Received by editor(s) in revised form: February 17, 2001
- Published electronically: March 8, 2002
- Additional Notes: This research was partially supported by Hungarian National Research Grant T 032455.
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 2413-2417
- MSC (2000): Primary 03E05
- DOI: https://doi.org/10.1090/S0002-9939-02-06309-8
- MathSciNet review: 1897467