We consider a finite permutation group acting naturally on a vector space V​​ over a field k​​. A well known theorem of Göbel asserts that the corresponding ring of invariants k[V]^G​​ is generated by invariants of degree at most dim V choose 2​​.  We point out that if the characteristic of k​​ is zero then the top degree of the vector coinvariants k[mV]_G​​ is also bounded above by n choose 2​​ implying that Göbel's bound almost holds for vector invariants as well in characteristic zero.
This work is joint with F. Reimers.