I'm trying to recall a theorem I saw once about metabelian groups -- it was either of the form "Every metabelian group satisfies..." or of the form "Every group satisfying ... is metabelian".
What was significant/surprising about it was that even though the problem had been open for a while, the proof ultimately just consisted of a few lines of algebraic manipulations (an exception to Scott Aaaronson's number 6).
Unfortunately that's all I remember. Does anyone have any idea what I might be referring to? Thanks!
Edit: It may have been showing that semidirect products of a certain form are metabelian? Not sure. (Now that we have the answer, it wasn't, though this was close.)