On the p-rank of the ideal class group of a normal extension with simple Galois group
Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 3, pp. 671-678.

Let p be a prime and L a finite normal extension over a number field K whose Galois group is simple and non-abelian. The aim of this paper is to estimate a lower bound of the ratio of the p-rank of the ideal class group of L to the p-rank of the ambiguous p-class group of L with respect to K.

Soient p un nombre premier et L une extension normale finie d’un corps de nombres K dont le groupe de Galois est simple et non abélien. Le but de cet article est d’estimer la borne inférieure du quotient du p-rang du groupe de classes d’idéaux de L par le p-rang du groupe de p-classes ambiges de L par rapport à K.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1101
Classification: 11R29,  20D06,  20D08
Keywords: Class group, simple group
Yutaka Konomi 1

1 Department of Mathematics Meijo University Tempaku-ku, Nagoya 468-8502, Japan
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Yutaka Konomi. On the $p$-rank of the ideal class group of a normal extension with simple Galois group. Journal de Théorie des Nombres de Bordeaux, Volume 31 (2019) no. 3, pp. 671-678. doi : 10.5802/jtnb.1101. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1101/

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[2] Yutaka Konomi On p-class group of an A n -extension, Proc. Japan Acad., Volume 84 (2008) no. 7, pp. 87-88 | Article | MR: 2450056 | Zbl: 1192.11077

[3] G. N. Thwaites The Abelian p-subgroups of GL(n,p) of maximal rank, Bull. Lond. Math. Soc., Volume 4 (1972), pp. 313-320 | Article | MR: 318319 | Zbl: 0262.20054

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