Questions tagged [galois-theory]
The study of connections between field theory and group theory through the idea of Galois groups and further concepts.
6
votes
2answers
171 views
How did the modern understanding of Galois theory come about?
The "modern" understanding of the Galois group of a polynomial is as automorphisms of the splitting field of the polynomial which keep the base field fixed. These concepts were unknown to Galois, who ...
2
votes
1answer
102 views
Did Galois make use of the concept of a basis?
I've been reading Galois' First Memoir, where he introduces Galois Theory by giving a sufficient and necessary condition for a polynomial to be solvable by radicals. The proofs are a bit sketchy and ...
9
votes
1answer
445 views
History of Galois Theory after Galois
Galois theory occupies a rather central place in modern number theory, from class field theory, to the Langlands program, to the ideas found in Grothendieck's Esquisse d'un Programme. But the ...
11
votes
2answers
750 views
Did Evariste Galois create the entire group structure concept?
Did Evariste Galois create the entire group structure concept?
If yes, were "super-sets" of groups (e.g. rings or vector
spaces) created on top of Galois's work? When and by who?
If no, did Galois ...
3
votes
0answers
80 views
Who is the first to give the proof of insolvability of quintic functions using Galois theory?
The first correct proof of the insolvability of the quintic is due to Abel. But my question is who gave the proof of insolvability of the quintic using Galois theory? Does Abel know about Galois ...
12
votes
1answer
371 views
What does Lagrange mean in this passage from Reflexions sur la résolution?
I'm having difficulty with section 6 of Lagrange's Réfléxions sur la résolution algébrique des équations. That's page 11 of the paper, 215 of his Oeuvres. Annoyingly, this is one of the most critical ...
13
votes
1answer
175 views
When was the modern field theory approach to Galois theory developed?
It is well known that Galois, and other mathematicians around that time, considered Galois groups to be permutation groups and approached Galois theory in this manner. At some point the theory took a ...
