8 problems.
- Presentation of a semidirect product Z_m ⋊_φ Z_n
- Normal subgroup and abelianness for a group of order p(p+1)
- Minimal polynomial degree for an algebraic element over a finite field
- Every finite group appears as a Galois group over some field extension
- Splitting field and Galois group of \(x^4-5\) over \(\QQ\)
- A matrix with A^3 = A decomposes C^n into a direct sum of three subspaces
- Equivalent conditions for a finite-dimensional quotient of a polynomial ring
- Intersection of noetherian ring quotients is noetherian