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