On 2-extensions of the rationals with restricted ramification

Peter Schmid. "On 2-extensions of the rationals with restricted ramification." Acta Arithmetica 163.2 (2014): 111-125. <http://eudml.org/doc/278917>.

@article{PeterSchmid2014,
abstract = {For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside \{2,∞\}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication).},
author = {Peter Schmid},
journal = {Acta Arithmetica},
keywords = {Galois theory; restricted ramification; central group and field extensions; Schur multipliers; ring class fields},
language = {eng},
number = {2},
pages = {111-125},
title = {On 2-extensions of the rationals with restricted ramification},
url = {http://eudml.org/doc/278917},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Peter Schmid
TI - On 2-extensions of the rationals with restricted ramification
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 2
SP - 111
EP - 125
AB - For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside {2,∞}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication).
LA - eng
KW - Galois theory; restricted ramification; central group and field extensions; Schur multipliers; ring class fields
UR - http://eudml.org/doc/278917
ER -