arXiv (OAI Expanded)
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Noether's problem for $A_6$ and $A_7$
We prove that $B_kA_6$ is stably rational over every field $k$ in which $2$ and $-3$ are nonzero squares. Combining this with a theorem of Plans, we deduce that $B_kA_7$ is stably rational over every field $k$ of characteristic zero in which $2$ and $-3$ are squares.
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