Title:  Why is Nakajima's theorem true, and why is there a counter example by Stong?
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Abstract:  The Shephard-Todd/Chevalley theorem states that a nonmodular ring of polynomial invariants
of a finite group is polynomial if and only the group can be generated by pseudoreflections.
The "only if" part remains true for any ground fields as proven by Serre. The "if" part
is wrong in the modular case: Nakajima studied this intensively and presented many 
very obnoxious examples. However, he also gave a sufficient and necessary criterion 
for modular p-group representations to have polynomial invariants. Alas, his proof works only
over the prime field. And even worse, Stong gave an example that Nakajima's
characterization is wrong for larger ground fields. We study why Stong's example 
exists and how to generalize Nakajima's theorem.