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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1997 • Question 5

Question

Math 6310 • Algebra Fall 1997 • Question 5

Let \(H\) be a proper subgroup of the finite group \(G\). Prove that \(G\) has a conjugacy class \(C\) such that \(C\) contains no element of \(H\).

Raw LaTeX

Let \(H\) be a proper subgroup of the finite group \(G\). Prove that \(G\) has a conjugacy class \(C\)
such that \(C\) contains no element of \(H\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups