Simultaneous representations of groups (Q1201252)
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scientific article; zbMATH DE number 97503
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Simultaneous representations of groups |
scientific article; zbMATH DE number 97503 |
Statements
Simultaneous representations of groups (English)
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17 January 1993
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It is proved that for any finite sequence of groups \(G_ 0\subseteq G_ 1\subseteq\cdots\subseteq G_ n\) there exists an undirected graph \((V,E)\) such that \(G_ i\) is isomorphic to the automorphism group of the graph \((V,E^{2^ i})\). This extends some results by \textit{R. Frucht} [Compos. Math. 6, 239-250 (1938; Zbl 0020.07804)] and \textit{G. Sabidussi} [Monatsh. Math. 64, 64-67 (1960; Zbl 0097.389)].
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representations of groups
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automorphism group
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