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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Kharazishvili, Aleksander (2015-11-18T12:34:03Z)
Acta Universitatis Lodziensis. Folia Mathematica
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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...
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...
Martin Ziegler, Rüdiger Göbel (1988/89)
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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Janusz Dronka, Bronislaw Wajnryb, Paweł Witowicz, Kamil Orzechowski (2017)
Open Mathematics
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We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.
Carlo Toffalori (2000)
Rendiconti del Seminario Matematico della Università di Padova
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Peter H. Schmitt (1984)
Mémoires de la Société Mathématique de France
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Luise-Charlotte Kappe, M. J. Tomkinson (1998)
Rendiconti del Seminario Matematico della Università di Padova
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Paul Hill, Charles Megibben (1985)
Mathematische Zeitschrift
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C. Calderón (2003)
Publications de l'Institut Mathématique
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J. L. Brenner, M. Randall, J. Riddell (1974)
Colloquium Mathematicae
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