The Broué conjecture for the faithful 3-blocks of 4 . M₂₂

We verify Broué's conjecture for the faithful 3-blocks of defect 2 of the non-split central extension of the sporadic simple Mathieu group M₂₂ by a cyclic group of order 4. The proof is based on a strategy due to Okuyama and Rickard, where a stable equivalence is lifted to a derived equivalence. The stable equivalence in turn is provided by exploiting a result due to Puig. To handle this particular example, next to theoretical investigations we apply a whole bunch of computational tools.