The Galois number

1997 ◽  
Vol 309 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Pat W. Beaulieu ◽  
Tommy C. Palfrey
Keyword(s):  
Galois Number

scholarly journals Galois number fields with small root discriminant

2007 ◽  
Vol 122 (2) ◽  
pp. 379-407 ◽  
Author(s):  
John W. Jones ◽  
David P. Roberts
Keyword(s):  
Number Fields ◽  
Small Root ◽  
Galois Number

On the galois number and the minimal degree of doubly transitive groups

2000 ◽  
Vol 28 (10) ◽  
pp. 4889-4900 ◽  
Author(s):  
Martin Epkenhans ◽  
Oliver Gerstengarbe
Keyword(s):  
Minimal Degree ◽  
Transitive Groups ◽  
Galois Number ◽  
Doubly Transitive Groups

A note on the least prime that splits completely in a nonabelian Galois number field

2018 ◽  
Vol 292 (1-2) ◽  
pp. 183-192
Author(s):  
Zhenchao Ge ◽  
Micah B. Milinovich ◽  
Paul Pollack
Keyword(s):  
Number Field ◽  
Galois Number

Pre-Pólya group in even dihedral extensions of ℚ

2020 ◽  
pp. 2150001
Author(s):  
Abbas Maarefparvar
Keyword(s):  
Field Theory ◽  
Number Theory ◽  
Upper Bound ◽  
Dihedral Group ◽  
American Mathematical Society ◽  
Number Fields ◽  
Manuscripta Math ◽  
Galois Number ◽  
Dihedral Extensions ◽  
Special Case

Investigating on Pólya groups [P. J. Cahen and J. L. Chabert Integer-Valued Polynomials, Mathematical Surveys and Monographs, Vol. 48 (American Mathematical Society, Providence, 1997)] in non-Galois number fields, Chabert [J. L. Chabert and E. Halberstadt, From Pólya fields to Pólya groups (II): Non-Galois number fields, J. Number Theory (2020), https://doi.org/10.1016/j.jnt.2020.06.008 ] introduced the notion of pre-Pólya group [Formula: see text], which is a generalization of the pre-Pólya condition, duo to Zantema [H. Zantema, Integer valued polynomials over a number field, Manuscripta Math. 40 (1982) 155–203]. In this paper, using class field theory, we describe the pre-Pólya group of a [Formula: see text]-field [Formula: see text], for [Formula: see text] an even integer, where [Formula: see text] denotes the dihedral group of order [Formula: see text]. Moreover, for special case [Formula: see text], we improve the Zantema’s upper bound on the maximum ramification in Pólya [Formula: see text]-fields.

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