TWISTED CONJUGACY IN LINEAR ALGEBRAIC GROUPS

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