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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2015 • Question 3

Question

Math 6310 • Algebra Spring 2015 • Question 3

Let \(H\) be a proper subgroup of a finite group \(G\). Prove that \(\displaystyle \bigcup _{g\in G}gHg^{-1}\) does not equal \(G\).

Raw LaTeX

Let \(H\) be a proper subgroup of a finite group \(G\). Prove that
\(\displaystyle\bigcup_{g\in G}gHg^{-1}\) does not equal \(G\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups