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On Indices of Septic Number Fields Defined by Trinomials x 7 + ax + b

Author

Listed:
  • Lhoussain El Fadil

    (Department of Mathematics, Faculty of Sciences Dhar El Mahraz-Fes, Sidi Mohamed Ben Abdellah University, Fez P.O. Box 1796, Morocco)

Abstract

Let K be a septic number field generated by a root, α , of an irreducible trinomial, x 7 + a x + b ∈ Z [ x ] . In this paper, for every prime integer, p , we calculate ν p ( i ( K ) ) ; the highest power of p dividing the index, i ( K ) , of the number field, K . In particular, we calculate the index, i ( K ) . In application, when the index of K is not trivial, then K is not monogenic.

Suggested Citation

  • Lhoussain El Fadil, 2023. "On Indices of Septic Number Fields Defined by Trinomials x 7 + ax + b," Mathematics, MDPI, vol. 11(21), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4441-:d:1268180
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