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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2016 • Question 1

Question

Math 6310 • Algebra Summer 2016 • Question 1

Let \(G\) be a group (not necessarily finite), and suppose that \(H\) is a subgroup of index \(n\). Show that there is a normal subgroup \(N\) of \(G\) with \(n!\ge [G:N]\ge n\).

Raw LaTeX

Let \(G\) be a group (not necessarily finite), and suppose that \(H\) is a subgroup of index \(n\).
Show that there is a normal subgroup \(N\) of \(G\) with \(n!\ge [G:N]\ge n\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups