Abstract
For a transitive subgroup G ≤ S 6 which contain C 3 × C 3 as subgroup, we prove that K(x 1,…, x 6) G is rational over K, where K is any field, and G acts naturally on K(x 1,…, x 6) by permutations on the variables. We also give an application on construction of generic polynomials.
2010 Mathematics Subject Classification:
Notes
1We remark that there is a misprint in [Citation3] for T6.10 (p. 60), the λ′ = (1542)(36) there should be replaced by λ = (1425)(36) here, for otherwise λ′σ1λ′ = (14652) is of order 5 in T6.10, absurd.
2For 1 ≤ m ≤ p
k
− 1, the rational number is always a p-adic integer, and
. Therefore,
.
Communicated by J. Zhang.