Karagüzel, ÇisilYılmaz, Deniz2025-02-272025-02-272024-01-09https://hdl.handle.net/11693/116910Let $k$ be an algebraically closed field of characteristic $2$, let $G$ be a finite group and let $B$ be the principal $2$-block of $kG$ with a dihedral or a generalised quaternion defect group $P$. Let also $\calT(B)$ denote the group of splendid Morita auto-equivalences of $B$. We show that $$\begin{align*} \calT(B)\cong \Out_P(A)\rtimes \Out(P,\calF), \end{align*}$$ where $\Out(P,\calF)$ is the group of outer automorphisms of $P$ which stabilize the fusion system $\calF$ of $G$ on $P$ and $\Out_P(A)$ is the group of algebra automorphisms of a source algebra $A$ of $B$ fixing $P$ modulo inner automorphisms induced by ($A^P)^\times$.EnglishBlockFusion systemPicard groupDihedral defect groupGeneralised quaternion defect groupArticle10.24330/ieja.14029471306-6048