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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2003 • Question 19

Question

Math 6510 • Differentiable Manifolds Fall 2003 • Question 19

Let \(F_n\) be a 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 a 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