The Brauer indecomposability of Scott modules with wreathed 2-group vertices

Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

“…We choose this defect group for its many similarities with the tame cases. In this respect, from the group theory point of view, we strongly rely on the facts that the wreathed 2-groups C 2 n ≀ C 2 have 2-rank 2 and an automorphism group which is a 2-group, whereas from the modular representation theory point of view we rely on the Brauer indecomposability of Scott modules with wreathed vertices proved by the first author and Tuvay in [KT21].…”