Rationality problem for norm one tori in small dimensions

Abstract

We classify stably/retract rational norm one tori in dimension $n-1$ for $n=2^e$ $(e\ge 1)$ is a power of $2$ and $n=12,14,15$. Retract non-rationality of norm one tori for primitive $G\le S_{2p}$ where $p$ is a prime number and for the five Mathieu groups $M_n\le S_n$ $(n=11,12,22,23,24)$ is also given.

20 pages. The title was changed according to the editor's suggestion. arXiv admin note: substantial text overlap with arXiv:1811.01676, arXiv:1210.4525