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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2010 • Question 2

Question

Math 6310 • Algebra Fall 2010 • Question 2

Let \(G\) be the subgroup of \(\operatorname {GL}_2(\mathbb {R})\) consisting of matrices of the form \[ \begin {pmatrix} a & c\\ 0 & b \end {pmatrix}. \] Is \(G\) solvable?

Raw LaTeX

Let \(G\) be the subgroup of \(\operatorname{GL}_2(\mathbb{R})\) consisting of matrices of the form
\[
\begin{pmatrix}
a & c\\
0 & b
\end{pmatrix}.
\]
Is \(G\) solvable?

Topic Tags

Finite Group Theory Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization Normal Subgroups and Commutator Subgroups Solvable Groups