Twisted conjugacy and quasi‐isometry invariance for generalized solvable Baumslag–Solitar groups

By J. Taback, Peter Wong. 2006

51 citations recorded by the source corpus.

We say that a group has property R∞ if any group automorphism has an infinite number of twisted conjugacy classes. Fel'shtyn and Gonçalves proved that the solvable Baumslag‐Solitar groups BS(1, m) have property R∞. We define a solvable generalization Γ(S) of these groups which is shown to have property R∞. It is also shown that property R∞ is geometric for these groups, that is, any group quasi‐isometric to Γ(S) has property R∞ as well.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0cd12c80bea41b88a1658f0aa5faa0f371ee7548

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In Discrete Mathematics and Combinatorics

1. E. Troitsky
2. Alexander Fel'shtyn

In Geometry and Topology

1. E. Troitsky
2. Alexander Fel'shtyn
3. Peter Wong

In Mathematical Physics

1. E. Troitsky
2. Alexander Fel'shtyn
3. Peter Wong

Citations in the corpus

• Twisted Burnside-Frobenius theory for discrete groups (2006, methodology): “[5], [30], [6], [29], [43]) while in the ‘‘opposite’’ case the twisted Burnside theorem is proved we hope that various use of Theorem 3.”
• Twisted conjugacy classes in nilpotent groups (2007, unknown): “, [7], [8], [11], [18], [23], [28], and [29]).”