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Five degrees of separation

Author(s): Péter Komjáth
Journal: Proc. Amer. Math. Soc. 130 (2002), 2413-2417.
MSC (2000): Primary 03E05
Posted: March 8, 2002
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Abstract: If is an infinite Abelian group, $S\subseteq A \times A$ , then 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 $\min(\vert S\vert,\vert(A\times A)-S\vert)$ ).

References:

1.: M. Abért: Every infinite symmetric group is the product of finitely many Abelian groups, to appear.
2.: M. Abért, T. Keleti: Shuffle the plane, Proc. Amer. Math. Soc. 130 (2002), 549-553. CMP 2002:03.

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Additional Information:

Péter Komjáth
Affiliation: Department of Computer Science, Eötvös University, Budapest, P.O. Box 120, 1518, Hungary
Email: kope@cs.elte.hu

DOI: 10.1090/S0002-9939-02-06309-8
PII: S 0002-9939(02)06309-8
Received by editor(s): November 29, 2000
Received by editor(s) in revised form: February 17, 2001
Posted: March 8, 2002
Additional Notes: This research was partially supported by Hungarian National Research Grant T 032455.
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2002, American Mathematical Society


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