6 problems.
- A finite simple group with all proper subgroups abelian is cyclic of prime order
- Galois group of \(x^5-5a^4x+a\) over \(\QQ\)
- An outer automorphism of \(S_6\) from a transitive embedding \(S_5\hookrightarrow S_6\)
- Equivalence of \(\mathrm{Ann}(M)\not\subset\mathfrak{p}\), \(M_{\mathfrak{p}}=0\), and \(M\otimes_A k(\mathfrak{p})=0\) for finitely generated modules
- \(\CC[x,y]/(y^2-(x-1)^3-(x-1)^2)\) is a domain, its real points, and its integral closure
- A projective resolution of \(k\simeq R/(x,y)\) over \(R=k[x,y]\) and \(\mathrm{Tor}_i^R((x,y),k)\)