Definition:Galois Group of Field Extension/Topological Group

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Definition

The notation $\Gal {L / K}$ is also a shorthand for the topological group:

$\struct {\Gal {L / K}, \tau}$

where $\tau$ is the Krull topology.


Also denoted as

The Galois group of $L / K$ can also be denoted $\map G {L / K}$.


Also known as

The Galois group of $L / K$ is also known as its automorphism group and denoted $\Aut {L / K}$.

Some authors refer to $\Aut {L / K}$ as a Galois group only when $L / K$ is a Galois extension.

Some sources use the notation $\map G {L \mid K}$.


Also see

  • Results about Galois groups of field extensions can be found here.


Source of Name

This entry was named for Évariste Galois.


Sources


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