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Abelian subgroups of any order in class groups of global function fields
- Source :
-
Journal of Number Theory . May2004, Vol. 106 Issue 1, p26. 24p. - Publication Year :
- 2004
-
Abstract
- Let <f>F</f> be a finite field with <f>q</f> elements, and <f>T</f> a transcendental element over <f>F</f>. In this paper, we construct infinitely many real function fields of any fixed degree over <f>F(T)</f> with ideal class numbers divisible by any given positive integer greater than 1. For imaginary function fields, we obtain a stronger result which shows that for any relatively prime integers <f>m</f> and <f>n</f> with <f>m,n>1</f> and relatively prime to the characteristic of <f>F</f>, there are infinitely many imaginary fields of fixed degree <f>m</f> such that the class group contains a subgroup isomorphic to <f>(Z/nZ)m−1</f>. [Copyright &y& Elsevier]
- Subjects :
- *RINGS of integers
*ISOMORPHISM (Mathematics)
*RING theory
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 106
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 12739068
- Full Text :
- https://doi.org/10.1016/j.jnt.2003.12.003