Free products of absolute Galois groups
type: Item
instance of: scholarly article
title: Free products of absolute Galois groups
zbMATH Open document ID: 0961.12002
published in: Doklady Mathematics
publication date: 2001-02-22T00:00:00Z
review text: The main goal of this paper under review is to give an affirmative answer to Problem 18 in \textit{M. Jarden}'s survey [Infinite Galois theory, Handbook of algebra. Vol. 1, 269-319 (1996; Zbl 0864.12003)]. This problem asks whether the free product of \(n\) absolute Galois groups of fields is also an absolute Galois group of a field. The author states the following theorem: Let the profinite groups \(G_1, \ldots, G_n\) be isomorphic to absolute Galois groups of fields. Then their free product \(G_1 \ast \cdots \ast G_n\) is also isomorphic to an absolute Galois group of a field of characteristic zero. Note that meanwhile a similar result concerning also the positive characteristic case is obtained by \textit{O. V. Mel'nikov} [Sib. Math. J. 40, No. 1, 95-99 (1999; Zbl 0935.12005)] using different methods.
reviewed by: Stefan Reiter
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 1568492
zbMATH Keywords: absolute Galois group
zbMATH Keywords: profinite group
zbMATH Keywords: free profinite product
author: Yuri L. Ershov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1568492