Theorem

Fundamental Theorem of Galois Theory

Algebra

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

Statement

For 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

Classification

Statement Form

Existence Theorem 1

Connections

Sources

1. Fundamental Theorem of Galois Theory (Wikipedia)

Wikimedia FoundationLead section, first sentence

Quote, Lead 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.

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Fundamental Theorem of Galois Theory

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