Normal generation of locally compact groups

Amichai Eisenmann, Nicolas Monod

Published 2012-06-28, updated 2012-07-02Version 2

It is a well-known open problem since the 1970s whether a finitely generated perfect group can be normally generated by a single element or not. We prove that the topological version of this problem has an affirmative answer as long as we exclude infinite discrete quotients (which is probably a necessary restriction).