7 problems.
- Faithful transitive actions: trivial core of a stabilizer, and abelian transitive subgroups of \(S_n\)
- Abelian groups of order 36, and nonabelian groups of order 36
- Irreducible factors of \(f(g(x))\) have degree a multiple of \(\deg f\), and of \(x^{2n}-r\) over \(\mathbb{Q}\) when \(r\) is not a square
- \(\QQ[\theta]\) for an \(S_4\)-quartic has no intermediate fields, unlike Galois extensions of degree \(4\)
- Commutative unital simple rings are fields, and \(M_n(k)\) is simple
- \(\ZZ[\sqrt{-5}]\) is not a PID: units \(\pm 1\), and \(3\) irreducible but not prime
- \(F[x]\)-modules of linear operators, similarity, and simplicity in dimension \(2\)