Twisted conjugacy classes in general and special linear groups.

DOI10.1007/s10469-012-9185-6zbMath1264.20046OpenAlexW1984520673MaRDI QIDQ1928480

Timur R. Nasybullov

Publication date: 3 January 2013

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-012-9185-6

zbMATH Keywords

general linear groupsautomorphism groupsintegral domainsspecial linear groupsnumbers of twisted conjugacy classes

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Fixed points and coincidences in algebraic topology (55M20) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (15)

The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups ⋮ Twisted conjugacy in classical Chevalley groups over certain domains of positive characteristic ⋮ Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups ⋮ Twisted conjugacy classes in twisted Chevalley groups ⋮ The \(R_\infty\)-property for Chevalley groups of types \(B_l\), \(C_l\), \(D_l\) over integral domains. ⋮ Twisted conjugacy in linear algebraic groups ⋮ Two examples related to the twisted Burnside-Frobenius theory for infinitely generated groups ⋮ Twisted conjugacy classes in unitriangular groups ⋮ Chevalley groups of types \(B_n\), \(C_n\), \(D_n\) over certain fields do not possess the \(R_{\infty}\)-property ⋮ Twisted Conjugacy Classes for Polyfree Groups ⋮ Twisted conjugacy and quasi-isometric rigidity of irreducible lattices in semisimple Lie groups ⋮ Twisted conjugacy classes in lattices in semisimple Lie groups ⋮ Reidemeister spectrum of special and general linear groups over some fields contains 1 ⋮ Twisted conjugacy in direct products of groups ⋮ Twisted conjugacy classes in Chevalley groups.

Cites Work

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• Twisted conjugacy classes in nilpotent groups.
• Twisted conjugacy classes in R. Thompson's group \(F\).
• Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups. (With an appendix written jointly with Francois Dahmani)
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• TWISTED CONJUGACY CLASSES IN WREATH PRODUCTS
• Twisted conjugacy classes in nilpotent groups
• Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
• The automorphisms of the linear groups over any integral domain.

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