Reachable elements in basic classical Lie superalgebras

Let g=g0¯⊕g1¯ be a basic classical Lie superalgebra over C, e∈g0¯ nilpotent element and ge the centralizer of e in g. We study various properties elements g, which have previously only been considered case algebras. In particular, we prove that is reachable if satisfies Panyushev property for g=sl(m|n), m≠n or psl(n|n) osp(m|2n). For exceptional superalgebras g=D(2,1;α), G(3), F(4), give classification are reachable, strongly satisfy property. addition, bases its centre z(ge) g=psl(n|n), completes results Han on relationship between dim⁡ge, dim⁡z(ge) labelled Dynkin diagrams all superalgebras.