Multiplicative groups of Galois extensions
type: Item
instance of: scholarly article
title: Multiplicative groups of Galois extensions
zbMATH Open document ID: 0798.12004
published in: Journal of Algebra
publication date: 1994-11-10T00:00:00Z
review text: The author obtains the following interesting results: Theorem. Let \(K\) be a Galois extension of \(k\) with Galois group \(G\) and suppose that \(G\) contains two dihedral subgroups \(D_ p\) and \(D_ q\) for distinct odd primes \(p\), \(q\). Then if \(F_ 1,\dots, F_ N\) are the maximal proper subfields of \(K/k\) then \(K^ \times= F_ 1^ \times \dots F_ N^ \times\). Corollary. If \(K\) is a Galois extension of \(k\) with Galois group \(S_ n\), \(n\geq 5\), then \(K^ \times\) is generated by the multiplicative subgroups of proper intermediate fields.
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 589930
zbMATH Keywords: Galois extension
zbMATH Keywords: dihedral subgroups
zbMATH Keywords: multiplicative subgroups
author: William J. Haboush
MaRDI profile type: Publication
full work available at URL: jabr.1994.1101
OpenAlex ID: W2093898732
DOI: 10.1006/JABR.1994.1101
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description: scientific article; zbMATH DE number 589930