The central polynomials for the finite dimensional Grassmann algebras

In this note we describe the central polynomials for the finite dimensional unitary Grassmann algebras $G_k$ over an infinite field $F$ of characteristic $\ne 2$. We exhibit a set of generators of $C(G_k)$, the T-space of the central polynomials of $G_k$ in a free associative $F$-algebra.