New York Journal of Mathematics
Volume 19 (2013) 117-129


David J. Fernández Bretón

Every strongly summable ultrafilter on ⊕Z2 is sparse

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Published: March 23, 2013
Keywords: ultrafilters, Stone-Čech compactification, sparse ultrafilter, strongly summable ultrafilter, finite sums, Boolean group, abelian group.
Subject: 03E75 (Primary); 54D35, 54D80 (Secondary).

We investigate the possibility of the existence of nonsparse strongly summable ultrafilters on certain abelian groups. In particular, we show that every strongly summable ultrafilter on the countably infinite Boolean group is sparse. This answers a question of Hindman, Steprans and Strauss.


The author would like to thank the support received from the Consejo Nacional de Ciencia y Tecnología (CONACyT), Mexico, by means of scholarship number 213921/309058.

Author information

Department of Mathematics and Statistics, York University, 4700 Keele St., Toronto, Ontario, Canada, M3J 1P3.