Twisted conjugacy in linear algebraic groups

2020/04/20 by Bhunia, Sushil, Bose, Anirban · 1 citation
#20G15 #FOS: Mathematics #Group Theory (math.GR) #Primary 20E45

paper · doi:10.48550/arxiv.2004.09635

Abstract

Let k be an algebraically closed field, G a linear algebraic group over k and φ∈ Aut(G), the group of all algebraic group automorphisms of G. Two elements x, y of G are said to be φ-twisted conjugate if y=gxφ(g)^-1 for some g∈ G. In this paper we prove that for a connected non-solvable linear algebraic group G over k, the number of its φ-twisted conjugacy classes is infinite for every φ∈ Aut(G).

Cited by

• Twisted conjugacy classes in Lie groups

Related

• Twisted Conjugacy in Linear Algebraic Groups II
• Twisted conjugacy classes in twisted Chevalley groups
• Twisted conjugacy classes in special and general linear groups
• Twisted Conjugacy in Big Mapping Class Groups
• The R_∞ and S_∞ properties for linear algebraic groups