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Automorphism groups of complements of points. (English) Zbl 0829.20052

For a given group \(G\), two directed graphs (or metrizable topological spaces) \(K_1\) and \(K_2\) are given such that the automorphism groups of \(K_1\) and \(K_2\) consist of the identity map, and for any \(x\in K_1\), the automorphism group of \(K_1\setminus\{x\}\) is isomorphic to \(G\), and there exists \(x_G\in K_2\) such that the automorphism group of \(K_2\setminus\{x_G\}\) is isomorphic to \(G\), and for any \(x\in K_2\setminus\{x_G\}\), the automorphism group of any \(K_2\setminus\{x\}\) consists of the identity.
Reviewer: V.Koubek (Praha)

MSC:

20F29 Representations of groups as automorphism groups of algebraic systems
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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