On minus quotients of ideal class groups of cyclotomic fields

• FUJII, Satoshi

Abstract

Let [Formula: see text] be the minus quotient of the ideal class group of the [Formula: see text]th cyclotomic field. In this paper, first, we show that each finite abelian group appears as a subgroup of [Formula: see text] for some [Formula: see text]. Second, we show that, for all pairs of integers [Formula: see text] and [Formula: see text] with [Formula: see text], the kernel of the lifting map [Formula: see text] is contained in the [Formula: see text]-torsion [Formula: see text] of [Formula: see text]. Such an evaluation of the exponent is an individuality of cyclotomic fields.

Journal

• International Journal of Number Theory

  International Journal of Number Theory 16 (9), 2013-2026, 2020-06-16

  World Scientific Pub Co Pte Lt

Keywords

• Cyclotomic fields
• ideal class groups
• minus quotients
• capitulations

Details

• CRID: 1050289697214529664
• NII Article ID: 120007159678
• DOI: 10.1142/s1793042120501043
• ISSN: 17937310
• ISSN: 17930421
• Web Site: http://ir.lib.shimane-u.ac.jp/53835
• Web Site: https://www.worldscientific.com/doi/pdf/10.1142/S1793042120501043
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN