On the Reidemeister spectrum and the R_∞ property for some free nilpotent groups

2009/03/26 by Kukina, E. G., Roman'kov, V.
#20E36 #20E45 #20F10 #20F18 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0903.4533

Abstract

We describe the Reidemeister spectrum Spec_RG for G = N_rc, the free nilpotent group of rank r and class c, in the cases: r ∈ \mathbb N and c = 1; r = 2, 3 and c = 2; r = 2 and c = 3, and prove that any group N_2c for c ≥ 4 satisfies to the R_∞ property. As a consequence we obtain that every free solvable group S_2t of rank 2 and class t ≥ 2 (in particular the free metabelian group M₂ = S₂₂ of rank 2) satisfies to the R_∞ property. Moreover, we prove that any free solvable group S_rt of rank r ≥ 2 and class t big enough also satisfies to the R_∞ property.

Related

• Extreme Reidemeister spectra of finite groups
• Reidemeister spectrum for metabelian groups of the form Qⁿ\rtimes \mathbb Z and \mathbb Z[1/p]ⁿ\rtimes \mathbb Z, p prime
• The Reidemeister spectrum of low dimensional almost-crystallographic groups
• Reidemeister spectra of free nilpotent groups and plethysms of Schur functions
• The R_∞--property for nilpotent quotients of Baumslag--Solitar groups