On the towers of torsion Bertrandias and Payan modules

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Abstract

For an odd prime p, let K/k be a Galois p-extension and S be a set of primes of k containing the primes lying over p. For the prth roots μpr(K) of unity in K, we describe the so-called Sha group ShaS(G(K/k), μpr(K)) in terms of the Galois groups of certain subfields of K corresponding to S. As an application, we investigate a tower of extension fields kTii≥0 where kTi+1 is defined as the fixed field of a free part of the Galois group of the Bertrandias and Payan extension of kTi over kTi. This is called a tower of torsion parts of the Bertrandias and Payan extensions over k. We find a relation between the degrees {[kTi+1:kTi]}i≥0 over the towers. Using this formula we investigate whether the towers are stationary or not.

Original languageEnglish
Pages (from-to)563-583
Number of pages21
JournalIsrael Journal of Mathematics
Volume221
Issue number2
DOIs
Publication statusPublished - 2017 Sep 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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