Farjoun's nilpotence-preservation conjecture for group localizations

Let $L$ be a localization on the category of groups, meaning a functor equipped with a natural transformation from the identity satisfying the idempotence conditions for a localization. A group is nilpotent if it has a finite central series. Farjoun's nilpotence-preservation conjecture. Any localization on the category of groups sends a nilpotent group to a nilpotent group. This conjecture was formulated by Emmanuel Dror Farjoun in personal communication; its status is not resolved in the supplied source.