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

Carlo Toffalori

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)

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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...