Twisted Burnside-Frobenius theory for discrete groups

DOI10.1515/CRELLE.2007.097zbMath1204.20031arXivmath/0606179MaRDI QIDQ5459222

Evgenij V. Troitsky, Alexander Fel'shtyn

Publication date: 25 April 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606179

zbMATH Keywords

numbers of conjugacy classesautomorphismsirreducible representationspolycyclic groupsFC-groupsconjugacy separable groupsReidemeister classesnumbers of fixed pointsBurnside-Frobenius theorem

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Solvable groups, supersolvable groups (20F16) Geometric group theory (20F65) Unitary representations of locally compact groups (22D10) Automorphisms of infinite groups (20E36)

Related Items (28)

Pólya-Carlson dichotomy for dynamical zeta functions and a twisted Burnside-Frobenius theorem ⋮ The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups ⋮ Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups ⋮ The twisted commutator subgroups and questions of Fel'shtyn and Troitsky ⋮ Fixed points and stable images of endomorphisms for the free group of rank two ⋮ Twisted conjugacy classes in nilpotent groups. ⋮ New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory ⋮ Reidemeister classes and twisted inner representations. ⋮ Minimizing the number of periodic points for smooth maps. Non-simply connected case ⋮ Reidemeister classes in some weakly branch groups ⋮ Erratum to: ``Twisted Burnside-Frobenius theory for discrete 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 classes in some lamplighter-type groups ⋮ Twisted conjugacy classes in saturated weakly branch groups. ⋮ Dynamical zeta functions of Reidemeister type and representations spaces ⋮ Twisted conjugacy classes in unitriangular groups ⋮ CRYPTANALYSIS OF USHAKOV — SHPILRAIN’S AUTHENTICATION PROTOCOL BASED ON THE TWISTED CONJUGACY PROBLEM ⋮ Dynamical zeta functions of Reidemeister type ⋮ 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) ⋮ The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\) ⋮ Effective twisted conjugacy separability of nilpotent groups ⋮ Reidemeister classes in lamplighter-type groups ⋮ Twisted Burnside-Frobenius theorem and \(R_\infty\)-property for lamplighter-type groups ⋮ Twisted conjugacy in direct products of groups ⋮ Dold sequences, periodic points, and dynamics

Cites Work

• On the Burnside problem for periodic groups
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Conjugate separability in polycyclic groups
• Coincidence Reidemeister classes on nilmanifolds and nilpotent fibrations
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• Conjugacy Separability and Free Products of Groups with Cyclic Amalgamation
• A Characteristic Property of Soluble Groups
• Embedding Theorems for Groups
• Groups with Finite Classes of Conjugate Elements (In Memoriam Issai Schur)

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