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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Fall 2020 • Question 5

Question

Math 6520 • Algebraic Topology Fall 2020 • Question 5

Let \(G\) be a finite group of order \(d\) and \(\phi :F_n\to G\) an epimorphism from the free group of rank \(n\). Show that \(\operatorname {Ker}(\phi )\) is a free group and compute its rank.

Raw LaTeX

Let \(G\) be a finite group of order \(d\) and \(\phi:F_n\to G\) an epimorphism from
the free group of rank \(n\). Show that \(\operatorname{Ker}(\phi)\) is a free group and compute
its rank.

Topic Tags

Free Groups, Graph Coverings, and Presentations