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Vector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group 
$Z/p$ of prime order in characteristic 
$p$ the image of the transfer homomorphism 
$\text{T}{{\text{r}}^{Z/p}}\,:\,F[V]\,\to \,F{{[V]}^{Z/p}}$ is a prime ideal, and the quotient algebra 
$F{{[V]}^{Z/p}}/\,\text{IM(T}{{\text{r}}^{Z/p}})$ is a polynomial algebra on the top Chern classes of the action.
