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Klein resolvent for an equation of fifth degree over a field of characteristic dividing into 5!

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Abstract

Klein's familiar constructions of the single-parameter resolvent for an equation of fifth degree cannot be extended without modification to fields of characteristic 2, 3, or 5. It is shown that, for such fields, the single-parameter resolvent exists, and its construction is described.

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Literature cited

  1. F. Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichung vom fünften Grade, Leipzig (1884).

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Authors
  1. A. N. Gorbov
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  2. R. A. Shmidt
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 36–40, 1974.

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Gorbov, A.N., Shmidt, R.A. Klein resolvent for an equation of fifth degree over a field of characteristic dividing into 5!. J Math Sci 9, 318–322 (1978). https://doi.org/10.1007/BF01085049

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  • DOI: https://doi.org/10.1007/BF01085049

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