Abstract

An infinite group G is said to have property Ro if every automorphism p e Aut(G) hasR(yp)= co where R(y) denotes the cardinality of the set of orbits of the (left) action of G on G viao. a +> aap(o)-1. The study of (in)finiteness of R(yp) has its origin in Nielsen fixed point theory.In this talk, l will give an overview of existing results on property Ro together with some openquestions.