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Bulletin of the London Mathematical Society Advance Access originally published online on April 1, 2008
Bulletin of the London Mathematical Society 2008 40(2):337-346; doi:10.1112/blms/bdn015
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© 2008 London Mathematical Society

Finite groups in Stone–Cech compactifications

Yevhen Zelenyuk

School of Mathematics
University of the Witwatersrand
Private Bag 3
Wits 2050
South Africa

Received 23 January 2007. Revision received 26 October 2007.

Let {kappa} be an infinite cardinal and let G = {oplus}{kappa}Z2. Now let β G be the Stone–Cech compactification of G as a discrete semigroup, and let H{kappa}={cap}{alpha}<{kappa}c{ell}β G {xisinG\{0}:minsupp (x)≥{alpha}}. We show that the semigroup H{kappa} contains no nontrivial finite group.

2000 Mathematics Subject Classification 20M10, 22A30 (primary); 20M15, 54H11 (secondary).


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