scholarly journals On the exponents of ideal class groups of cyclotomic fields

1993 ◽  
Vol 119 (4) ◽  
pp. 1049-1049 ◽  
Author(s):  
Kuniaki Horie
Keyword(s):  
Cyclotomic Fields ◽  
Ideal Class ◽  
Class Groups ◽  
Ideal Class Groups

On minus quotients of ideal class groups of cyclotomic fields

2020 ◽  
Vol 16 (09) ◽  
pp. 2013-2026
Author(s):  
Satoshi Fujii
Keyword(s):  
Abelian Group ◽  
Class Group ◽  
Finite Abelian Group ◽  
Cyclotomic Field ◽  
Cyclotomic Fields ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Class Groups ◽  
Ideal Class Groups ◽  
The Ideal

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.

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