Difference between revisions
inverse-galois
Status and infobox
- status:
—→ open - kind:
—→ problem - year:
—→ 1850 - statement:
—→ Is every finite group the Galois group of some extension of the rational numbers?
Source +21 −0
+---
+title: Inverse Galois problem
+kind: problem
+status: open
+year: 1850
+statement: Is every finite group the Galois group of some extension of the rational numbers?
+space: algebra
+---
+Known for solvable groups (Shafarevich) and for all but one of the sporadic groups; the Mathieu group M23 is the famous holdout. Most methods use rigidity, building extensions from the geometry of covering spaces.
+
+Posed 19th century; systematic work from Hilbert and Emmy Noether.
+
+## What would settle it
+
+Lean statement in formal-conjectures
+
+## Sources
+
+- [Wikipedia: Inverse Galois problem](https://en.wikipedia.org/wiki/Inverse_Galois_problem)
+
+[[Space:algebra|Algebra and groups]] · [[Continent:mathematics|Mathematics]]
Revision 53 as rendered
Known for solvable groups (Shafarevich) and for all but one of the sporadic groups; the Mathieu group M23 is the famous holdout. Most methods use rigidity, building extensions from the geometry of covering spaces.
Posed 19th century; systematic work from Hilbert and Emmy Noether.
What would settle it
Lean statement in formal-conjectures