TITLE: Ore's Conjecture for perfect groups
QUESTION [9 upvotes]: We know that Ore's Conjecture is a theorem now. Does anyone know a counterexample to Ore's conjecture for perfect groups? I believe there should be one, but I dont have a counterexample. Thanks.

REPLY [5 votes]: An old paper of mine (Amer. Math. Monthly 1977) gives an easy way to
construct groups where not every element of the derived subgroup is
a commutator. In particular, if $U$ is a large enough abelian group
and $H$ is a simple group, then the derived subgroup of the wreath
product of $U$ by $H$ is perfect and contains non-commutators.