Prime factors of class number of cyclotomic fields
Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 525-530.

Soit p un nombre premier impair, r une racine primitive modulo p et r i r i (modp) avec 1r i p-1. En 2007, R. Queme a posé la question : le -rang ( premier impair p) du groupe des classes d’idéaux du p-ième corps cyclotomique est-il égal au degré du plus grand diviseur commun sur le corps fini 𝔽 de x (p-1)/2 +1 et du polynôme de Kummer f(x)= i=0 p-2 r -i x i . Dans cet article, nous donnons une réponse complète à cette question en produisant un contre-exemple.

Let p be an odd prime, r be a primitive root modulo p and r i r i (modp) with 1r i p-1. In 2007, R. Queme raised the question whether the -rank ( an odd prime p) of the ideal class group of the p-th cyclotomic field is equal to the degree of the greatest common divisor over the finite field 𝔽 of x (p-1)/2 +1 and Kummer’s polynomial f(x)= i=0 p-2 r -i x i . In this paper, we shall give the complete answer for this question enumerating a counter-example.

DOI : 10.5802/jtnb.639
Taniguchi, Tetsuya 1

1 Department of Mathematics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
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Taniguchi, Tetsuya. Prime factors of class number of cyclotomic fields. Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 2, pp. 525-530. doi : 10.5802/jtnb.639. http://www.numdam.org/articles/10.5802/jtnb.639/

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