7 problems.
- For any group \(G\) we define \(\Omega(G)\) to be the image of the group
- Order of \(\mathrm{GL}_3(\mathbb{F}_2)\) and the number of elements of order \(7\)
- The kernel of a surjection \(\ZZ^m\to G\) onto a finite abelian group is isomorphic to \(\ZZ^m\), with \(|\det A|=|G|\)
- Units and maximal ideals of \(C[0,1]\)
- Inverse images of primes are prime, the nilradical is contained in every prime, and \(\mathrm{Spec}(R/N)\to\mathrm{Spec}(R)\) is bijective
- Irreducibility, degree, and Galois group of \(x^{10}+x^5+1\) over \(\QQ\)
- Generators of \(\mathbb F_{p^6}\) inside \(\mathbb F_{p^n}\)