Rationality problem for norm one tori, II

Sumito Hasegawa, Akinari Hoshi, Aiichi Yamasaki

Published 2018-11-06Version 1

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