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Generic Galois extensions for SL_2(F_5) over Q

Bernat Plans

2007Mathematics被引 2

摘要

Let Gn be a double cover of either the alternating group An or the sym- metric 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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