FC--ELEMENTS IN TOTALLY DISCONNECTED GROUPS AND AUTOMORPHISMS OF INFINITE GRAPHS

An element in a topological group is called an FC--element if its conjugacy class has compact closure. The FC--elements form a normal subgroup. In this note it is shown that in a compactly generated totally disconnected locally compact group this normal subgroup is closed. This result answers a ques...

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Bibliographic Details
Published in:Mathematica scandinavica 2003-01, Vol.92 (2), p.261-268
Main Author: MÖLLER, RÖGNVALDUR G.
Format: Article
Language:English
Subjects:
Automorphisms
Discrete mathematics
General topology
Mathematical lattices
Mathematical theorems
Orbitals
Topological compactness
Topological theorems
Topology
Vertices
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Summary:An element in a topological group is called an FC--element if its conjugacy class has compact closure. The FC--elements form a normal subgroup. In this note it is shown that in a compactly generated totally disconnected locally compact group this normal subgroup is closed. This result answers a question of Ghahramani, Runde and Willis. The proof uses a result of Trofimov about automorphism groups of graphs and a graph theoretical interpretation of the condition that the group is compactly generated.
ISSN:0025-5521
1903-1807
DOI:10.7146/math.scand.a-14404