On the existence of finite Galois stable groups over integers in unramified extensions of number fields

D. A. Malinin

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let E/F be a normal unramified number field extension with Galois group F of degree d, and let OE be the ring of integers in E. It is proved that for given integers n, t such that n ≥ hφE(t)d, where h is the exponent of the class group of F and φE(t) is the generalized Euler function, there is a finite abelian γ-stable subgroup G ⊂ GLn(OE) of exponent t such that the matrix entries of all g ∈ G generate E over F. This result has certain arithmetic applications for totally real extensions, and a construction of totally real extensions having a prescribed Galois group is given.

Original languageEnglish
Pages (from-to)179-191
Number of pages13
JournalPublicationes Mathematicae
Volume60
Issue number1-2
Publication statusPublished - Jan 1 2002

Keywords

  • Algebraic integers
  • Galois algebras
  • Galois group
  • Integral representations
  • Unramified extensions

ASJC Scopus subject areas

  • Mathematics(all)

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