The property R∞R_{\infty} conjecture for finitely presented SS-arithmetic subgroups of Borel groups

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Let B\mathbf{B} be a Borel subgroup of a split, connected, reductive, non-commutative linear algebraic group G\mathbf{G}, all defined over a global field. An SS-arithmetic subgroup is finitely presented if it admits a finite presentation, and a group has property R∞R_{\infty} if every automorphism has infinitely many twisted conjugacy classes. Property R∞R_{\infty} conjecture. All finitely presented SS-arithmetic subgroups of B\mathbf{B} which are not virtually polycyclic have property R∞R_{\infty}. This would extend the results for the soluble SS-arithmetic groups considered in the paper to Borel subgroups of split reductive groups; the claim is presented as a conjectural consequence of the geometric and algebraic structure discussed above, and no resolution is supplied here.

References

Primary source

Paula Macedo Lins de Araujo and Yuri Santos Rego, “Twisted conjugacy in soluble arithmetic groups”, arXiv:2007.02988 (2024).

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