Subgroups of free groups generated by conjugates of powers of the generators

摘要

For a free group F-n = < x(1), ... , x(n)> we investigate when a finite index subgroup of F-n is generated by a set X of powers of conjugates of the generators x(1), ..., x(n). For the braid group B-n = we similarly consider when a finite index subgroup is generated by a set of powers of Dehn twists, i.e., conjugates of the elements sigma(2)(i). We indicate a connection of these problems with the theory of c-groups developed by Burnside, Schur and Wielandt.