The geometry of twisted conjugacy classes in wreath products

Details The geometry of twisted conjugacy classes in wreath products The geometry of twisted conjugacy classes in wreath products

2008-05-09

arxiv.org/abs/0805.1371v2

in: Geometry, Rigidity, and Group Actions, Chicago Lectures in Mathematics (2011), 561-587

Mathematics

Group Theory

19 pages, 4 figures

Scientific paper

We give a geometric proof based on recent work of Eskin, Fisher and Whyte that the lamplighter group $L_n$ has infinitely many twisted conjugacy classes for any automorphism $\vp$ only when $n$ is divisible by 2 or 3, originally proved by Gon\c{c}alves and Wong. We determine when the wreath product $G \wr \Z$ has this same property for several classes of finite groups $G$, including symmetric groups and some nilpotent groups.

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