Primitive elements in subgroups of free groups

Abstract

Question F39 on the World of Groups list of open problems reads: (a) Is there an algorithm which, when given a finitely generated subgroup S of a free group F and an element g of F, decides whether or not there is an automorphism of F that takes g to an element of the subgroup S? (b) The following special case of part (a) is especially attractive: given a finitely generated subgroup S of a free group F, find out whether or not S contains a primitive element of F. In this talk, we provide an algorithm to answer part (b) of this question.