On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent

Carlo Toffalori

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Displaying similar documents to “On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent”

Some conditions implying that an infinite group is abelian

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

Rendiconti del Seminario Matematico della Università di Padova

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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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An elementary class extending abelian-by- $G$ groups, for $G$ 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 $G$ the class of abelian-by- $G$ groups is elementary, but, at least when $G$ is an infinite elementary abelian $p$ -group (with $p$ prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to $G$ is elementary.

On elementary equivalence of abelian groups

Fred Clare (1976)

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...