Reidemeister spectrum of special and general linear groups over some fields contains 1

DOI10.1142/S0219498819501536OpenAlexW2963728594MaRDI QIDQ5230120

Timur R. Nasybullov

Publication date: 20 August 2019

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.06280

zbMATH Keywords

widthlinear groupstwisted conjugacy classesReidemeister numberReidemeister spectrum

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Linear algebraic groups over arbitrary fields (20G15) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Related Items (7)

Twisted conjugacy in linear algebraic groups. II ⋮ Twisted conjugacy classes in twisted Chevalley groups ⋮ Structure and automorphisms of pure virtual twin 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 ⋮ Automorphisms of odd Coxeter groups ⋮ Some remarks on twin groups

Cites Work

• The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups
• Twisted conjugacy classes of the unit element.
• Every invertible matrix is diagonally equivalent to a matrix with distinct eigenvalues
• The \(R_{\infty}\) property for abelian groups
• Aspects of the property \(R_\infty\).
• The \(R_\infty\)-property for Chevalley groups of types \(B_l\), \(C_l\), \(D_l\) over integral domains.
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• The Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite.
• Twisted conjugacy classes in general and special linear groups.
• Twisted conjugacy classes in Chevalley groups.
• Most automorphisms of a hyperbolic group have very simple dynamics
• Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups
• Automorphisms of the Complex Numbers
• Endomorphisms of linear algebraic groups
• On groups where the twisted conjugacy class of the unit element is a subgroup

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