The Kummerian property and maximal pro-p Galois groups

Ido Efrat, Claudio Quadrelli

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

For a prime number p, we give a new restriction on pro-p groups G which are realizable as the maximal pro-p Galois group G F (p) for a field F containing a root of unity of order p. This restriction arises from Kummer Theory and the structure of the maximal p-radical extension of F. We study it in the abstract context of pro-p groups G with a continuous homomorphism θ:G→1+pZ p , and characterize it cohomologically, and in terms of 1-cocycles on G. This is used to produce new examples of pro-p groups which do not occur as maximal pro-p Galois groups of fields as above.

Original languageEnglish
Pages (from-to)284-310
Number of pages27
JournalJournal of Algebra
Volume525
DOIs
StatePublished - 1 May 2019

Keywords

  • Cyclotomic pro-p pairs
  • Galois cohomology
  • Galois groups
  • Kummer theory
  • Maximal pro-p Galois groups
  • Pro-p groups

ASJC Scopus subject areas

  • Algebra and Number Theory

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