Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Winter 2007 • Question 13

Question

Math 6510 • Differentiable Manifolds Winter 2007 • Question 13

Let \(F_n\) be the free group of rank \(n\) and let \(G\subset F_n\) be a subgroup of index \(m\). Prove that \(G\) is a free group and compute its rank.

Raw LaTeX

Let \(F_n\) be the free group of rank \(n\) and let \(G\subset F_n\) be a subgroup of
index \(m\). Prove that \(G\) is a free group and compute its rank.

Topic Tags

Free Groups, Graph Coverings, and Presentations