On covers of abelian groups by cosets
Günter Lettl, Zhi-Wei Sun (2008)
Acta Arithmetica
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Günter Lettl, Zhi-Wei Sun (2008)
Acta Arithmetica
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Krzysztof Krupiński (2005)
Fundamenta Mathematicae
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Anne C. Morel (1968)
Colloquium Mathematicae
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Fred Clare (1976)
Colloquium Mathematicae
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Z. Daróczy, I. Kátai (1985)
Aequationes mathematicae
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Kharazishvili, Aleksander (2015-11-18T12:34:03Z)
Acta Universitatis Lodziensis. Folia Mathematica
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H. Stetkaer (1997)
Aequationes mathematicae
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Roland Coghetto (2015)
Formalized Mathematics
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We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset of a subgroup, index of a subgroup, conjugation, normal subgroup, topological group, dense...
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...
Artūras Dubickas (2003)
Acta Arithmetica
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Hartman, S.
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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.
R.C. Alperin, R.K. Dennis, R. Oliver (1987)
Inventiones mathematicae
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