Permanence properties of the second nilpotent product of groups

• Autores: Sasyk, Roman
• Año de publicación: 2019
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: SECOND NILPOTENT PRODUCT OF GROUPS; WREATH PRODUCT OF GROUPS; GROUPS WITH THE HAAGERUP PROPERTY; GROUPS WITH THE KAZDHAN'S PROPERTY (T); EXACT GROUPS
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

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.
Fil: Sasyk, Roman. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina