On finite galois stable subgroups of gln in some relative extensions of number fields

H. J. Bartels, D. A. Malinin

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Let K/ℚ be a finite Galois extension with maximal order OK and Galois group Γ. For finite Γ-stable subgroups G ⊂ GLn OK) it is known [4], that they are generated by matrices with coefficients in OK ab, K ab the maximal abelian subextension of K over ℚ. This note gives a contribution to the corresponding question in the case of a relative Galois extension K/R, where R is a finite extension of the rationals ℚ. It turns out, that in this relative situation the answer to the corresponding question depends heavily on the arithmetic of the number field R, more precisely on the ramification behavior of primes in K/R. Due to the possibility of unramified extensions of R for certain number fields R there exist examples of Galois stable linear groups G ⊂ GLn (OK) which are not fixed elementwise by the commutator subgroup of Gal (K/R).

Original languageEnglish
Pages (from-to)493-503
Number of pages11
JournalJournal of Algebra and its Applications
Volume8
Issue number4
DOIs
Publication statusPublished - 2009

Keywords

  • Algebraic number theory
  • Class numbers
  • Integral representations of finite groups
  • Integral representations related to algebraic numbers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On finite galois stable subgroups of gln in some relative extensions of number fields'. Together they form a unique fingerprint.

Cite this