A Step Beyond Kemperman's Structure Theorem

David J. Grynkiewicz

Type: Article

Publication Date: 2009-12-01

Citations: 30

DOI: https://doi.org/10.1112/s0025579300000966

Abstract

MathematikaVolume 55, Issue 1-2 p. 67-114 Research Article A Step Beyond Kemperman's Structure Theorem David J. Grynkiewicz, David J. Grynkiewicz [email protected] Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, AustriaSearch for more papers by this author David J. Grynkiewicz, David J. Grynkiewicz [email protected] Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, AustriaSearch for more papers by this author First published: 01 December 2009 https://doi.org/10.1112/S0025579300000966Citations: 10AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract We extend Kemperman's structure theorem by completely characterizing those finite subsets A and B of an arbitrary abelian group with |A + B| = |A| + |B|. Citing Literature Volume55, Issue1-2December 2009Pages 67-114 RelatedInformation

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Works Cited by This (32)

Action	Title	Year	Authors
+	On a generalization of a theorem by Vosper.	2000	Oriol Serra Gilles Zémor
+	Hyper-atoms and the Kemperman's critical pair Theory	2007	Yahya Ould Hamidoune
+	Hyper-atoms and the critical pair Theory	2008	Yahya Ould Hamidoune
+	Ein Satz �ber abelsche Gruppen mit Anwendungen auf die Geometrie der Zahlen	1954	Martin Kneser
+	Subsets with a Small Sum II: the Critical Pair Problem	2000	Yahya Ould Hamidoune
+	The Erdős-Heilbronn problem in Abelian groups	2004	Gyula Károlyi
+	Subsets with Small Sums in Abelian Groups' I: the Vosper Property	1997	Yahya Ould Hamidoune
+	A Generalisation of the Theorem of Cauchy and Davenport	1974	J. M. Pollard
+	CRITICAL PAIRS IN ABELIAN GROUPS AND KEMPERMAN'S STRUCTURE THEOREM	2006	Vsevolod F. Lev
+	Summenmengen in lokalkompakten abelschen Gruppen	1956	Martin Kneser