Notes on the existence of unramified non-abelian p-extensions over cyclic fields

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Abstract

We study the inverse Galois problem with restricted ramifications. Let p and q be distinct odd primes such that p≡1modq . Let E(p 3 ) be the non-abelian group of order p 3 such that the exponent is equal to p , and let k be a cyclic extension over Q of degree q . In this paper, we study the existence of unramified extensions over k with the Galois group E(p 3 ) . We also give some numerical examples computed with PARI.

Journal

  • Proceedings of the Japan Academy Series A: Mathematical Sciences

    Proceedings of the Japan Academy Series A: Mathematical Sciences 90(4), 67-70, 2014-01-01

    Japan Academy = 日本学士院

Codes

  • NII Article ID (NAID)
    120005440335
  • NII NACSIS-CAT ID (NCID)
    AA00785474
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0386-2194
  • Data Source
    IR 
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