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The K-admissibility of SL(2, 5)

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Paul Feit

  2. Department of Mathematics, Yale University, Yale Station, Box 2155, 06520, New Haven, CT, USA

    Walter Feit

Authors
  1. Paul Feit
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  2. Walter Feit
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Additional information

Dedicated to Professor Jacques Tits on the occasion of his sixtieth birthday

The first author was partly supported by NSF fellowship DMS-8601130; the second author was partly supported by NSF grant DMS-8806371.

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Feit, P., Feit, W. The K-admissibility of SL(2, 5). Geom Dedicata 36, 1–13 (1990). https://doi.org/10.1007/BF00181462

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  • DOI: https://doi.org/10.1007/BF00181462

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