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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2015 • Question 4

Question

Math 6310 • Algebra Spring 2015 • Question 4

Set \(G=GL_2(\mathbb {C})\). Construct a proper subgroup \(H\) of \(G\) such that \(\displaystyle \bigcup _{g\in G}gHg^{-1}\) equals \(G\).

Raw LaTeX

Set \(G=GL_2(\mathbb{C})\). Construct a proper subgroup \(H\) of \(G\) such that
\(\displaystyle\bigcup_{g\in G}gHg^{-1}\) equals \(G\).

Topic Tags

Finite Group Theory Normal Subgroups and Commutator Subgroups