Classes réalisables par des extensions métacycliques non abéliennes et éléments de Stickelberger

✍ Scribed by Bouchaı̈b Sodaı̈gui

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 321 KB
• Volume: 65
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1997.2133

✦ Synopsis

Let k be a number field, O k its ring of integers, 1 a nonabelian metacyclic group of order lq, where l, q are prime numbers. Assume that k and the lq th cyclotomic field of Q are linearly disjoint over

, Cl(M) its class group. We determine the set of elements of Cl(M) which are realizable by some tamely ramified extensions with Galois groups isomorphic to 1 using some Stickelberger elements, and we prove that it is a subgroup of Cl(M).

1997 Academic Press berger,'' ce qui lui a permis de montrer que

Dans cet article, on s'inte resse au cas non abe lien. On se place dans la situation suivante: 1 est un groupe me tacyclique d'ordre lq, ouÁ l et q sont article no. NT972133 87 0022-314XÂ97 25.00