Establishes an order-reversing bijection between the intermediate fields of a finite Galois field extension and the subgroups of its Galois group. Building on the work of Evariste Galois, it turns questions about field extensions and polynomial solvability into questions about finite group structure.
Facts
StatementFor a finite Galois field extension E over F, there is a one-to-one, inclusion-reversing correspondence between the intermediate fields of the extension and the subgroups of its Galois group. 1 Proof Method Classification
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Source Fundamental Theorem of Galois Theory (Wikipedia)
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1. Fundamental Theorem of Galois Theory (Wikipedia)
Wikimedia FoundationLead section, first sentence
the fundamental theorem of Galois theory is a result that describes the structure of certain types of field extensions in relation to groups.
Principal Result Of: Évariste Galois, Lead sentence of the article on the result
It was proved by Évariste Galois in his development of Galois theory.
In Group: Field Theory and Galois Theory, Lead section
In mathematics, the fundamental theorem of Galois theory is a result that describes the structure of certain
View the Source 2. ProofWiki: Fundamental Theorem of Galois Theory
ProofWikiProof sectionQuote, Proof section
Aiming for a contradiction, suppose there exists $\alpha \in L_{G_F} \setminus F$.
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