2 problems

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Noether's rationality conjecture for permutation invariants
Let $k$ be a field, let $x_1,\dots,x_k$ be variables, and let $G$ be a finite group acting by permutation on these variables. Noether's rationality conjecture. The invariant field…
Conjecturerefutedinvariant-fields inverse-galois-theory rationality-problemarXiv posted 2 days ago
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Pure transcendence conjecture for invariant fields of groups of order $p^5$
Let $p$ be a prime, let $G$ be a group of order $p^5$ , and let $V$ be a faithful finite-dimensional complex representation of $G$ . The invariant field is $\mathbb{C}(V)^G$ , where…
Conjectureopenfinite-groups invariant-fields noethers-problemarXiv posted 2 days ago

Noether's rationality conjecture for permutation invariants