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december 2019 Permanence properties of the second nilpotent product of groups
Román Sasyk
Bull. Belg. Math. Soc. Simon Stevin 26(5): 725-742 (december 2019). DOI: 10.36045/bbms/1579402819

Abstract

We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a semi-direct product akin to the restricted wreath product but constructed from the second nilpotent product. We then show that if two discrete groups have the Haagerup property, the restricted second nilpotent wreath product of them also has the Haagerup property. We finally show that if a discrete group is abelian, then the restricted second nilpotent wreath product constructed from it is unitarizable if and only if the acting group is amenable.

Citation

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Román Sasyk. "Permanence properties of the second nilpotent product of groups." Bull. Belg. Math. Soc. Simon Stevin 26 (5) 725 - 742, december 2019. https://doi.org/10.36045/bbms/1579402819

Information

Published: december 2019
First available in Project Euclid: 19 January 2020

zbMATH: 07167753
MathSciNet: MR4053850
Digital Object Identifier: 10.36045/bbms/1579402819

Subjects:
Primary: 20E22, 20F19, 20F65

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 5 • december 2019
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