4 problems

Let $G$ be a finite solvable group. Central-extension rationality conjecture. There exists a central extension … with a faithful representation $V$ of $G^c$ such that $V/G^c$ is ra…

Let $G$ be a finite group. Rational-quotient conjecture. There exists a $k$-rational $G$-variety $X$ with a generically free $G$-action such that $X/G$ is $k$-rational. This is a n…

Let $A$ be a finite abelian group, let $F^c(A)$ be its free central extension, and let $V$ be a faithful linear representation of $F^c(A)$ over an algebraically closed field $k$. F…

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…