IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Permanence properties of the second nilpotent product of groups
Autor/es:
ROMAN SASYK
Revista:
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN
Editorial:
BELGIAN MATHEMATICAL SOC TRIOMPHE
Referencias:
Año: 2019 vol. 26 p. 725 - 742
ISSN:
1370-1444
Resumen:
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.