Class groups of dihedral extensions

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Lemmermeyer F.

MATHEMATISCHE NACHRICHTEN, vol.278, no.6, pp.679-691, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 278 Issue: 6
  • Publication Date: 2005
  • Doi Number: 10.1002/mana.200310263
  • Journal Name: MATHEMATISCHE NACHRICHTEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.679-691
  • Keywords: class groups, dihedral extension, unramilied extensions, reflection theorems, embedding problems, 3-CLASS GROUPS, EXISTENCE, 4-RANK
  • Middle East Technical University Affiliated: No

Abstract

Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let KIF and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k).