Open Access
2015 Property of rapid decay for extensions of compactly generated groups
Lukasz Garncarek
Publ. Mat. 59(2): 301-312 (2015).


n the article we settle down the problem of permanence of property RD under group extensions. We show that if $1\to N\to G\to Q\to 1$ is a short exact sequence of compactly generated groups such that $Q$ has property RD, and $N$ has property RD with respect to the restriction of a word-length on $G$, then $G$ has property RD.

We also generalize the result of Ji and Schweitzer stating that locally compact groups with property RD are unimodular. Namely, we show that any automorphism of a locally compact group with property RD which distorts distances subexponentially, preserves the Haar measure.


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Lukasz Garncarek. "Property of rapid decay for extensions of compactly generated groups." Publ. Mat. 59 (2) 301 - 312, 2015.


Published: 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1321.22009
MathSciNet: MR3374609

Primary: 20F65 , 22D15 , 43A15

Keywords: Group extension , Property RD

Rights: Copyright © 2015 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.59 • No. 2 • 2015
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