Infinite Free Products of Profinite Groups as Absolute Galois Groups

Moshe Jarden

doi:10.1080/00927872.2025.2455449

Infinite Free Products of Profinite Groups as Absolute Galois Groups

Moshe Jarden^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

It is known that the free product of finitely many absolute Galois groups of fields is the absolute Galois group of a field. We give examples of free products of infinitely many nontrivial absolute Galois groups of fields which are not isomorphic to the absolute Galois group of any field. On the other hand, we give examples of free products of infinitely many nontrivial absolute Galois groups of fields which are the absolute Galois group of a field.

Original language	English
Pages (from-to)	3107-3110
Number of pages	4
Journal	Communications in Algebra
Volume	53
Issue number	8
DOIs	https://doi.org/10.1080/00927872.2025.2455449
State	Published - 2025

Keywords

Absolute Galois groups
Infinite free products
Profinite groups

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10.1080/00927872.2025.2455449

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abstract = "It is known that the free product of finitely many absolute Galois groups of fields is the absolute Galois group of a field. We give examples of free products of infinitely many nontrivial absolute Galois groups of fields which are not isomorphic to the absolute Galois group of any field. On the other hand, we give examples of free products of infinitely many nontrivial absolute Galois groups of fields which are the absolute Galois group of a field.",

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KW - Profinite groups

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Infinite Free Products of Profinite Groups as Absolute Galois Groups

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Keywords

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