3 problems. An irreducible of degree \(7\) over \(K\) with no zeros in a Galois extension \(L\) remains irreducible in \(L[x]\) Galois group of an irreducible of degree \(n\) embeds in \(S_n\); examples with \(G=S_n\), and the cubic case Exactly two groups of order 21 Browse these problems in source order