For linearly reductive finite group schemes, invariant rings are generated in degree at most the order of the group scheme, while for α_q the required degree is unbounded.
Fogarty, On Noether's bound for polynomial invariants of a finite group, Electron
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On Noether's Degree Bound for Finite Group Schemes
For linearly reductive finite group schemes, invariant rings are generated in degree at most the order of the group scheme, while for α_q the required degree is unbounded.