Zwei Aspekte konstruktiver Galoistheorie. (Two aspects of constructive Galois theory)

DOI10.1016/0021-8693(85)90024-9zbMath0587.12004OpenAlexW2130453797MaRDI QIDQ1072592

B. Heinrich Matzat

Publication date: 1985

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(85)90024-9

zbMATH Keywords

Mathieu grouparithmetic fundamental groupspecial linear groupalgebraic fundamental groupSL(2,q)\(M_{22}\)\(M_{12}\)inverse problem of Galois theory, algebraic function field

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Simple groups: sporadic groups (20D08) Galois theory (11R32) Representations of groups as automorphism groups of algebraic systems (20F29) Finite simple groups and their classification (20D05) Coverings in algebraic geometry (14E20)

Related Items (8)

Realization of sporadic simple groups as Galois groups over cyclotomic fields. ⋮ Realization of the Mathieu groups \(M_{11}\) and \(M_{12}\) as Galois groups over \({\mathbb Q})\). ⋮ Unnamed Item ⋮ Polynomials for primitive nonsolvable permutation groups of degree d\(\leq 15\) ⋮ Nearly ordinary Galois deformations over arbitrary number fields ⋮ Frattini-Einbettungsprobleme über Hilbertkörpern. (Frattini embedding problems over Hilbert fields) ⋮ 𝑃𝑆𝐿₂(𝑞) and extensions of 𝐐(𝐱) ⋮ Realisierung endlicher Gruppen als Galoisgruppen. (Realization of finite groups as Galois groups)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some finite groups which appear as Gal L/K, where \(K\subseteq {\mathbb{Q}}(\mu _ n)\)
• Konstruktion von Zahlkörpern mit der Galoisgruppe \(M_{12}\) über \(Q(\sqrt{-5})\)
• On the construction of Galois extensions of function fields and number fields
• Fundamentalgruppen algebraischer Mannigfaltigkeiten. (Fundamental groups of algebraic varieties)
• Galois properties of points of finite order of elliptic curves
• Konstruktion von Zahl- und Funktionenkörpern mit vorgegebener Galoisgruppe.
• On extensions of the maximal cyclotomic field having a given classical Galois group.
• ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
• Algebraic number fields

This page was built for publication: Zwei Aspekte konstruktiver Galoistheorie. (Two aspects of constructive Galois theory)