Covering theorems for finite non-abelian simple groups, I
J. L. Brenner, M. Randall, J. Riddell (1974)
Colloquium Mathematicae
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J. L. Brenner, M. Randall, J. Riddell (1974)
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)
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Kharazishvili, Aleksander (2015-11-18T12:34:03Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Breda d'Azevedo, Antonio J., Jones, Gareth A. (2000)
Beiträge zur Algebra und Geometrie
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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...
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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Kenichi Arai, Hiroyuki Okazaki, Yasunari Shidama (2012)
Formalized Mathematics
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In this article, we formalize that every finite cyclic group is isomorphic to a direct product of finite cyclic groups which orders are relative prime. This theorem is closely related to the Chinese Remainder theorem ([18]) and is a useful lemma to prove the basis theorem for finite abelian groups and the fundamental theorem of finite abelian groups. Moreover, we formalize some facts about the product of a finite sequence of abelian groups.
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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Steven Galovich, Sherman Stein (1981)
Aequationes mathematicae
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