Non-simple localizations of finite simple groups
  Often a localization functor (in the category of groups) sends a finite simple group to another finite simple group. We study when such a localization also induces a localization between the automorphism groups and between the universal central extensions. As a consequence we exhibit many examples of localizations of finite simple groups which are not simple. 
Jos\'e L. Rodr\'iguez (Almer\'ia, Spain), J\'er\^ome Scherer   (Barcelona, Spain), Antonio Viruel (M\'alaga, Spain)