Let G be a group and ϕ an automorphism of G. The ϕ-twisted conjugacy action of G on itself is given by the map (g, x) → gxϕ(g)^-1, for all g, x ∈ G and let R(ϕ) denote the cardinality of the set of all orbits of this action. In this talk we will consider such an action in the case of a linear algebraic group G over an algebraically closed field, describe conditions under which R(ϕ) is infinite for every automorphism ϕ of G and identify certain classes of groups which admit an automorphism ϕ such that R(ϕ) is finite. This is joint work with Sushil Bhunia.

Dr. Anirban Bose is an assistant professor at the department of mathematics of SRM University, Andhra Pradesh. He obtained his PhD from ISI, Delhi in 2014. His research revolves around algebraic groups and related structures. He has published in journals such as Journal of Algebra.