Geometriae Dedicata

, Volume 36, Issue 1, pp 1-13

First online:

The K-admissibility of SL(2, 5)

  • Paul FeitAffiliated withDepartment of Mathematics, Princeton University
  • , Walter FeitAffiliated withDepartment of Mathematics, Yale University

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Let K be a field and let G be a finite group. G is K-admissible if there exists a Galois extension L of K with G=Gal(L/K) such that L is a maximal subfield of a central K-division algebra. We characterize those number fields K such that H is K-admissible where H is any subgroup of SL(2, 5) which contains a S 2-group. The method also yields refinements and alternate proofs of some known results including the fact that A 5 is K-admissible for every number field K.