The rank of the group of relative units of a Galois extension. II
type: Item
instance of: scholarly article
title: The rank of the group of relative units of a Galois extension. II
zbMATH Open document ID: 1063.11037
author: Yoshitaka Odai
author: Hiroshi Suzuki
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2005-03-21T00:00:00Z
review text: Let \(L/K\) be a finite Galois extension of number fields with Galois group \(G\). Let \(n_G\) denote the \(\mathbb R\)-dimension of \(\bigcap_H\ker\text{Tr}_H\), where \(H\) ranges through the subgroups \(\neq1\) of \(G\) and \(\text{Tr}_H\) is the left \(G\)-endomorphism \(x\mapsto x\sum_{h\in H}h\) of the group ring \(\mathbb R[G]\). In Part I [Tohoku Math. J., II. Ser. 53, No. 1, 37--54 (2001; Zbl 0992.11061)], the authors computed the value of \(n_G\) for all groups \(G\) with the exception of two particular families. In the present paper they close the gap by showing that \(n_G=0\) for \(G= \text{SL}(2,\mathbb F_p)\), where \(p\) is a Fermat prime greater than \(5\).
reviewed by: Veikko Ennola
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 20D99
zbMATH DE Number: 2148492
zbMATH Keywords: relative unit
zbMATH Keywords: Galois extension
zbMATH Keywords: rank
zbMATH Keywords: special linear group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1113246673
OpenAlex ID: W2048311120
cites work: The rank of the group of relative units of a Galois extension
DOI: 10.2748/TMJ/1113246673
description: scientific article; zbMATH DE number 2148492