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Abelian subgroups of any order in class groups of global function fields

✍ Scribed by Allison M. Pacelli

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 311 KB
Volume: 106
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2003.12.003

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✦ Synopsis

Let F be a finite field with q elements, and T a transcendental element over F: In this paper, we construct infinitely many real function fields of any fixed degree over FðTÞ 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 m and n with m; n41 and relatively prime to the characteristic of F; there are infinitely many imaginary fields of fixed degree m such that the class group contains a subgroup isomorphic to ðZ=nZÞ mÀ1 :

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