Theorem: for faithful finite group actions in characteristic not dividing the group order, β_field ≤ 2D_span + 1, and equality is attained.
Generic separation for modular invariants
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abstract
For modular indecomposable representations of a cyclic group $G$ of prime order $p$ we propose a list of polynomial invariants of degree $\leq 3$ that, together with a simple invariant of degree $p$, separate generic orbits and generate the field of rational invariants. A similar result is proven for decomposable representations of $G$.
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Generic orbits, normal bases, and generation degree for fields of rational invariants
Theorem: for faithful finite group actions in characteristic not dividing the group order, β_field ≤ 2D_span + 1, and equality is attained.