The R_∞ property for nilpotent quotients of generalized solvable Baumslag-Solitar groups

2022/08/04 by Sgobbi, Wagner C., Silva, Dalton C., Vendrúscolo, Daniel
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2208.02647

Abstract

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

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