Hatcher-Algebraic-Topology · Problem 1.A.13

The Fundamental Group

Mathematics — Graph Theory · graphs-and-free-groups

Problem

Let

x

be a nontrivial element of a finitely generated free group

F

. Show there is a finite-index subgroup

H \subset F

in which

x

is one element of a basis. [Exercises 4 and 10 may be helpful.]