Twisted conjugacy classes in saturated weakly branch groups.

DOI10.1007/s10711-008-9245-1zbMath1192.20018arXivmath/0606725OpenAlexW2025514974MaRDI QIDQ930526

Evgenij V. Troitsky, Alexander Fel'shtyn, Yuriy G. Leonov

Publication date: 30 June 2008

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606725

zbMATH Keywords

twisted conjugacy classesGrigorchuk groupGupta-Sidki groupReidemeister numbersBurnside-Frobenius theoremweakly branch groups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Geometric group theory (20F65) Unitary representations of locally compact groups (22D10) Automorphisms of infinite groups (20E36) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Fundamental group, presentations, free differential calculus (57M05)

Related Items (28)

The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups ⋮ Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups ⋮ Twisted conjugacy classes in twisted Chevalley groups ⋮ The twisted commutator subgroups and questions of Fel'shtyn and Troitsky ⋮ Twisted conjugacy classes in nilpotent groups. ⋮ Thompson-like groups, Reidemeister numbers, and fixed points ⋮ New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory ⋮ Reidemeister classes and twisted inner representations. ⋮ The \(R_\infty\)-property for Chevalley groups of types \(B_l\), \(C_l\), \(D_l\) over integral domains. ⋮ Twisted conjugacy in big mapping class groups ⋮ Reidemeister classes in some weakly branch groups ⋮ Automorphisms of the generalized Thompson's group Tn,r$T_{n,r}$ ⋮ Twisted conjugacy in linear algebraic groups ⋮ Reidemeister classes, wreath products, and solvability ⋮ A relationship between twisted conjugacy classes and the geometric invariants \(\Omega^n\). ⋮ Two examples related to the twisted Burnside-Frobenius theory for infinitely generated groups ⋮ REIDEMEISTER SPECTRUM FOR METABELIAN GROUPS OF THE FORM Qⁿ ⋊ ℤ AND ℤ[1/pⁿ ⋊ ℤ, p PRIME] ⋮ Twisted Conjugacy Classes for Polyfree Groups ⋮ The Reidemeister spectra of low dimensional crystallographic groups ⋮ New directions in Nielsen-Reidemeister theory ⋮ Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups. (With an appendix written jointly with Francois Dahmani) ⋮ Twisted conjugacy classes in lattices in semisimple Lie groups ⋮ Some remarks on twin groups ⋮ Reidemeister classes in lamplighter-type groups ⋮ The R _∞ property for free groups, free nilpotent groups and free solvable groups ⋮ Twisted Burnside-Frobenius theorem and \(R_\infty\)-property for lamplighter-type groups ⋮ An averaging formula for Nielsen numbers on infra-solvmanifolds ⋮ Twisted conjugacy classes in Chevalley groups.

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