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arXiv · 1402.1675

Rationality problem for transitive subgroups of S_8

Baoshan Wang·Jian Zhou
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Abstract

For any field K and any transitive subgroup G of S_8, let G acts naturally on K(x_1, . . ., x_8) by permutations of the variables, we prove that under some minor conditions K(x_1, . . ., x_8)^G is always K-rational except G is A_8 or G is isomorphic to PGL(2, 7). We pay special attentions on the characteristic 2 cases.

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Baoshan Wang, Jian Zhou. 2014-02-07. Rationality problem for transitive subgroups of S_8. https://arxiv.org/abs/1402.1675

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