On Noether's Degree Bound for Finite Group Schemes

This paper establishes Noether’s classical degree bound $\beta (G)\le \mathrm{\mid }G\mathrm{\mid }$ for finite and linearly reductive group schemes. On the other hand, we provide examples of infinitesimal group schemes where $\beta (G)$ is unbounded. We also generalize Molien’s formula to finite and linearly reductive group schemes.