The R-8 property for nilpotent quotients of Generalized Solvable Baumslag-Solitar groups

Author(s)

Sgobbi, Wagner C. ; Silva, Dalton C. ; Vendruscolo, Daniel

• Document type: Journal article
• Source: Journal of Group Theory; v. N/A, p. 15-pg., 2023-01-31.

Abstract

We say a group G has property R-infinity if the number R(phi) of twisted conjugacy classes is infinite for every automorphism phi of G. For such groups, the R-infinity-nilpotency degree is the least integer c such that G/gamma(c +1).G/ has property R-infinity. In this work, we compute the R-infinity-nilpotency degree of all Generalized Solvable Baumslag-Solitar groups euro n. Moreover, we compute the lower central series of gamma(n), write the nilpotent quotients gamma(n,c) = = gamma(n)/gamma(c +1 )(gamma(n)) as semidirect products of finitely generated abelian groups and classify which invertible integer matrices can be extended to automorphisms o gamma(n,c). (AU)

• FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 19/03150-0 - Geometric invariants of groups and property R-infinity
• Grantee: Wagner Carvalho Sgobbi
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 17/21208-0 - Geometric invariants of groups and property R-infinity.
• Grantee: Wagner Carvalho Sgobbi
• Support Opportunities: Scholarships in Brazil - Doctorate