GENERIC GALOIS EXTENSIONS FOR SL 2 ( F 5 ) OVER Q Bernat Plans
نویسنده
چکیده
Let Gn be a double cover of either the alternating group An or the symmetric group Sn, and let Gn−1 be the corresponding double cover of An−1 or Sn−1. For every odd n ≥ 3 and every field k of characteristic 0, we prove that the following are equivalent: (i) there exists a generic extension for Gn−1 over k, (ii) there exists a generic extension for Gn over k. As a consequence, there exists a generic extension over Q for the group f A5 ∼= SL2(F5).
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