Centralizers of Nilpotent Elements in Basic Classical Lie Superalgebras in Good Characteristic

Let $g=g_{\overline{0}}\oplus g_{\overline{1}}$ be a basic classical Lie superalgebra over an algebraically closed field $K$ whose characteristic $p>0$ is a good prime for $g$ . Let $G_{\overline{0}}$ be the reductive algebraic group over $K$ such that $\text{Lie}\left(G_{\overline{0}}\right)=g_{\overline{0}}$ . Suppose $e\in g_{\overline{0}}$ is nilpotent. Write $g^e$ for the centralizer of e in $g$ and $z\left(g^e\right)$ for the centre of $g^e$ . We calculate a basis for $g^e$ and $z\left(g^e\right)$ by using associated cocharacters $\tau :K^{\times }\to G_{\overline{0}}$ of e. In addition, we give the classification of e which are reachable, strongly reachable or satisfy the Panyushev property for exceptional Lie superalgebras $D(2,1;\alpha )$ , G(3) and F(4).