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2006 Amenable groups that act on the line
Dave Witte Morris
Algebr. Geom. Topol. 6(5): 2509-2518 (2006). DOI: 10.2140/agt.2006.6.2509

Abstract

Let Γ be a finitely generated, amenable group. Using an idea of É Ghys, we prove that if Γ has a nontrivial, orientation-preserving action on the real line, then Γ has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Γ has a faithful action on the circle, then some finite-index subgroup of Γ has the property that all of its nontrivial, finitely generated subgroups have infinite, cyclic quotients. It also means that every left-orderable, amenable group is locally indicable. This answers a question of P Linnell.

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Dave Witte Morris. "Amenable groups that act on the line." Algebr. Geom. Topol. 6 (5) 2509 - 2518, 2006. https://doi.org/10.2140/agt.2006.6.2509

Information

Received: 9 June 2006; Accepted: 1 September 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1185.20042
MathSciNet: MR2286034
Digital Object Identifier: 10.2140/agt.2006.6.2509

Subjects:
Primary: 20F60

Rights: Copyright © 2006 Mathematical Sciences Publishers

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