$FC^-$-elements in totally disconnected groups and automorphisms of infinite graphs
Keyword(s):
An element in a topological group is called an $\mathrm{FC}^-$-element if its conjugacy class has compact closure. The $\mathrm{FC}^-$-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.
1988 ◽
Vol 104
(1)
◽
pp. 47-64
2003 ◽
Vol 74
(2)
◽
pp. 267-286
◽
1997 ◽
Vol 55
(1)
◽
pp. 143-146
◽
1969 ◽
Vol 21
◽
pp. 655-659
◽
1985 ◽
Vol 38
(1)
◽
pp. 55-64
◽
Keyword(s):