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Solvable absolute Galois groups are metabelian

Abstract:

We show that solvable absolute Galois groups have an abelian normal subgroup such that the quotient is the direct product of two finite cyclic and a torsion-free procyclic group. In particular, solvable absolute Galois groups are metabelian. Moreover, any field with solvable absolute Galois group G admits a non-trivial henselian valuation, unless each Sylow-subgroup of G is either procyclic or isomorphic to Z 2 ⋊ Z/2Z. A complete classification of solvable absolute Gal...

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Publication status:
Published

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Publisher copy:
10.1007/s002220000117

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
INVENTIONES MATHEMATICAE More from this journal
Volume:
144
Issue:
1
Pages:
1-22
Publication date:
2001-04-01
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
Language:
English
Pubs id:
pubs:13515
UUID:
uuid:1dc4e017-9a05-4406-9e5e-160275ef694e
Local pid:
pubs:13515
Source identifiers:
13515
Deposit date:
2012-12-19

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