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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2000 • Question 5

Question

Math 6310 • Algebra Fall 2000 • Question 5

Let \(H\) be a proper subgroup of the finite group \(G\). Prove that there is an element \(x\) in \(G\) such that \(x\) is not conjugate in \(G\) to any element of \(H\).

Raw LaTeX

Let \(H\) be a proper subgroup of the finite group \(G\). Prove that there is an element \(x\) in \(G\)
such that \(x\) is not conjugate in \(G\) to any element of \(H\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups