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

Hrušák, M.

Acta Univ. Carol., Math. Phys. 35, No. 2, 23-31 (1994).

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.)

Keywords:

directed graphs; metrizable topological spaces; automorphism groups