8 problems.
- Jordan form of \(\begin{pmatrix}-3&3&-2\\-7&6&-3\\1&-1&2\end{pmatrix}\) and a conjugating matrix
- Degree, Galois group, and intermediate fields of \(\QQ(\sqrt{2}+\sqrt{5})/\QQ\)
- Sylow theorems, and groups of order 1225
- Short five lemma
- Orbit-stabilizer bijection \(G/G_x\simeq G\cdot x\), and nontriviality of \(Z(G)\) for finite \(p\)-groups
- A Galois extension of degree \(2015\) is an extension by radicals
- Elementary divisors and invariant factors of a given \(\QQ[x]\)-module
- Unique halves and centrality in a simple rng without zero-divisors or \(2\)-torsion