On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent
Carlo Toffalori (2000)
Rendiconti del Seminario Matematico della Università di Padova
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Displaying similar documents to “Some conditions implying that an infinite group is abelian”
On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent
An elementary class extending abelian-by- groups, for infinite
Carlo Toffalori (1996)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We show that for no infinite group the class of abelian-by- groups is elementary, but, at least when is an infinite elementary abelian -group (with prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to is elementary.
Characterization of abelian-by-cyclic 3-rewritable groups
A. Abdollahi, A. Mohammadi Hassanabadi (2004)
Rendiconti del Seminario Matematico della Università di Padova
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Small sets in uncountable Abelian groups
Kharazishvili, Aleksander (2015-11-18T12:34:03Z)
Acta Universitatis Lodziensis. Folia Mathematica
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On elementary equivalence of abelian groups
Fred Clare (1976)
Colloquium Mathematicae
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Structure and order structure in Abelian groups
Anne C. Morel (1968)
Colloquium Mathematicae
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Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups
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...
A property equivalent to commutativity for infinite groups
Federico Menegazzo (1992)
Rendiconti del Seminario Matematico della Università di Padova
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Some commutativity criteria
John C. Lennox, A. Mohammadi Hassanabadi, James Wiegold (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Abelian profinite groups
Krzysztof Krupiński (2005)
Fundamenta Mathematicae
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Group algebras with centrally metabelian unit groups.
Meena Sahai (1996)
Publicacions Matemàtiques
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Given a field K of characteristic p > 2 and a finite group G, necessary and sufficient conditions for the unit group U(KG) of the group algebra KG to be centrally metabelian are obtained. It is observed that U(KG) is centrally metabelian if and only if KG is Lie centrally metabelian.
Inverse zero-sum problems in finite Abelian p-groups
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...