On the Reidemeister spectrum and the $R_{\infty}$ property for some free nilpotent groups

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dc.creatorKukina, E. G.
dc.creatorRoman'kov, V.
dc.date2009-03-26
dc.date.accessioned2026-07-07T12:57:01Z
dc.date.available2026-07-07T12:57:01Z
dc.descriptionWe describe the Reidemeister spectrum $Spec_RG$ for $G = N_{rc},$ the free nilpotent group of rank $r$ and class $c,$ in the cases: $r \in {\mathbb N}$ and $c = 1;$ $r = 2, 3$ and $c = 2;$ $ r = 2$ and $c = 3,$ and prove that any group $N_{2c}$ for $c \geq 4$ satisfies to the $R_{\infty}$ property. As a consequence we obtain that every free solvable group $S_{2t}$ of rank 2 and class $t \geq 2$ (in particular the free metabelian group $M_2 = S_{22}$ of rank 2) satisfies to the $R_{\infty}$ property. Moreover, we prove that any free solvable group $S_{rt}$ of rank $r \geq 2$ and class $t$ big enough also satisfies to the $R_{\infty}$ property.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0903.4533
dc.identifierhttp://arxiv.org/abs/0903.4533
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224785
dc.subjectGroup Theory
dc.subject20F10; 20F18; 20E45; 20E36
dc.titleOn the Reidemeister spectrum and the $R_{\infty}$ property for some free nilpotent groups
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