in Mathematics, 37 mins ago, by
ÍgjøgnumMeg Here's a cool one: Let $k$ be a perfect field and $p$ a prime. Show that there exists an algebraic extension $k^{(p)}/k$ such that each finite subextension has degree prime to $p$ and such that $k^{(p)}/k$ has no non-trivial finite extensions of degree prime to $p$.