### 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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Krzysztof Krupiński (2005)

Fundamenta Mathematicae

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Fred Clare (1976)

Colloquium Mathematicae

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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...

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

Rendiconti del Seminario Matematico della Università di Padova

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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...

Günter Lettl, Zhi-Wei Sun (2008)

Acta Arithmetica

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Carlo Toffalori (2000)

Rendiconti del Seminario Matematico della Università di Padova

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Paul Hill, Charles Megibben (1985)

Mathematische Zeitschrift

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Peter H. Schmitt (1984)

Mémoires de la Société Mathématique de France

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A. Abdollahi, A. Mohammadi Hassanabadi (2004)

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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William J. Gray (1968)

Colloquium Mathematicae

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