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- W4306808519 abstract "We give a necessary and sufficient condition for the Hasse norm principle for field extensions $K/k$ when the Galois groups ${rm Gal}(L/k)$ of the Galois closure $L/k$ of $K/k$ are isomorphic to the Mathieu group $M_{11}$ of degree $11$ of order $7920$ or the Janko group $J_1$ of order $175560$ by determining $H^1(k,{rm Pic}, overline{X})=0$ or $mathbb{Z}/2mathbb{Z}$ for norm one tori $T=R^{(1)}_{K/k}(mathbb{G}_m)$ with a smooth $k$-compactification $X$ and $overline{X}=Xtimes_koverline{k}$. The result gives a first step towards understanding the all pictures of the Hasse norm principle for the $26$ sporadic simple groups." @default.
- W4306808519 created "2022-10-20" @default.
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- W4306808519 date "2022-10-17" @default.
- W4306808519 modified "2023-09-24" @default.
- W4306808519 title "Hasse norm principle for $M_{11}$ and $J_1$ extensions" @default.
- W4306808519 doi "https://doi.org/10.48550/arxiv.2210.09119" @default.
- W4306808519 hasPublicationYear "2022" @default.
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