### Structure and order structure in Abelian groups

Anne C. Morel (1968)

Colloquium Mathematicae

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Anne C. Morel (1968)

Colloquium Mathematicae

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Fred Clare (1976)

Colloquium Mathematicae

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Kharazishvili, Aleksander (2015-11-18T12:34:03Z)

Acta Universitatis Lodziensis. Folia Mathematica

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David B. Penman, Matthew D. Wells (2014)

Acta Arithmetica

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We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic...

Benjamin Girard (2010)

Colloquium Mathematicae

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We study the minimal number of elements of maximal order occurring in a zero-sumfree sequence over a finite Abelian p-group. For this purpose, and in the general context of finite Abelian groups, we introduce a new number, for which lower and upper bounds are proved in the case of finite Abelian p-groups. Among other consequences, our method implies that, if we denote by exp(G) the exponent of the finite Abelian p-group G considered, every zero-sumfree sequence S with maximal possible...

Paul Hill, Charles Megibben (1985)

Mathematische Zeitschrift

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Günter Lettl, Zhi-Wei Sun (2008)

Acta Arithmetica

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A. Abdollahi, A. Mohammadi Hassanabadi (2004)

Rendiconti del Seminario Matematico della Università di Padova

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Luise-Charlotte Kappe, M. J. Tomkinson (1998)

Rendiconti del Seminario Matematico della Università di Padova

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Carlo Toffalori (2000)

Rendiconti del Seminario Matematico della Università di Padova

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Steven Galovich, Sherman Stein (1981)

Aequationes mathematicae

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C. Calderón (2003)

Publications de l'Institut Mathématique

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Peter H. Schmitt (1984)

Mémoires de la Société Mathématique de France

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Martin Ziegler, Rüdiger Göbel (1988/89)

Mathematische Zeitschrift

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William J. Gray (1968)

Colloquium Mathematicae

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