Cellular covers of local groups

This is joint work with Ramon Flores. Emmanuel Dror Farjoun asked whether the composition of a localization and a cellularization functor is always idempotent. Ramon Flores gave a negative answer for such functors in the category of spaces. We provide now a group theoretical counter-example based on the intriguing computation by Ol’shanskii of the Schur multiplier of Burnside groups at large primes. I will start with definitions and examples of localization and cellularization before introducing the main characters in this story.