Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

We classify principal 2-blocks of finite groups G with Sylow 2-subgroups isomorphic to a wreathed 2-group C_{2^n}\wr C_2 with n\geq 2 up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig's Finiteness Conjecture holds for such blocks. Furthermore, we obtain a classification of... Show more