  We prove a product decomposition of the Zariski closure of the jet lifts of a
holomorphic map f from C into a semi-abelian variety A, provided that f is of
finite order. On the other hand, by giving an example of such a map f into a
three dimensional abelian variety we show that this product decomposition does
not hold in general; there was a gap in the proofs of some articles which
claimed that such a product decomposition is always true.
