On characterized subgroups of Abelian topological groups $X$ and the group of all $X$-valued null sequences

S. S. Gabriyelyan

Displaying similar documents to “On characterized subgroups of Abelian topological groups $X$ and the group of all $X$ -valued null sequences”

The dual group of a dense subgroup

William Wistar Comfort, S. U. Raczkowski, F. Javier Trigos-Arrieta (2004)

Czechoslovak Mathematical Journal

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Throughout this abstract, $G$ is a topological Abelian group and $\hat{G}$ is the space of continuous homomorphisms from $G$ into the circle group $𝕋$ in the compact-open topology. A dense subgroup $D$ of $G$ is said to determine $G$ if the (necessarily continuous) surjective isomorphism $\hat{G} ↠ \hat{D}$ given by $h \mapsto h | D$ is a homeomorphism, and $G$ is determined if each dense subgroup of $G$ determines $G$ . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable...

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.

Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$ . If $n$ is any positive integer, either odd or divisible by $4$ , then we prove that the subgroup $A^{n}$ is also quasinormal in $G$ .

Displaying similar documents to “On characterized subgroups of Abelian topological groups X and the group of all X -valued null sequences”

The dual group of a dense subgroup

An elementary class extending abelian-by- G groups, for G infinite

Abelian quasinormal subgroups of groups

Displaying similar documents to “On characterized subgroups of Abelian topological groups $X$ and the group of all $X$ -valued null sequences”

An elementary class extending abelian-by- $G$ groups, for $G$ infinite