Fundamental Theorem of Galois Theory

prog big band, hawaiian electropop · 4:14

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Lyrics

[Verse 1]
In the realm where extensions grow
Fields and groups begin to show
Hidden patterns intertwined
Mirror worlds of different kind
Take a Galois field extension
Build a bridge of comprehension
Every subgroup has a mate
In the fields that correlate

[Chorus]
Bigger groups mean smaller fields
Perfect correspondence yields
Normal subs to Galois lands
Structure dancing hand in hands
Flip the order, keep the bond
Mathematics corresponds
Two theories, one disguise
Mirror truth before our eyes

[Verse 2]
Map each subgroup to its fix
Elements that never mix
When you act upon a field
What stays put becomes revealed
Take each intermediate ground
Find the group that keeps it bound
Inverse functions, crystal clear
Make the correspondence dear

[Chorus]
Bigger groups mean smaller fields
Perfect correspondence yields
Normal subs to Galois lands
Structure dancing hand in hands
Flip the order, keep the bond
Mathematics corresponds
Two theories, one disguise
Mirror truth before our eyes

[Bridge]
Lagrange meets the degree formula here
Count the elements, make the picture clear
Bijection proved through careful calculation
Group and field in perfect correlation
What transfers to topology's domain
Fundamental groups maintain
Covering spaces, ideals to varieties
Secret sameness, different theories

[Chorus]
Bigger groups mean smaller fields
Perfect correspondence yields
Normal subs to Galois lands
Structure dancing hand in hands
Flip the order, keep the bond
Mathematics corresponds
Two theories, one disguise
Mirror truth before our eyes

[Outro]
Build correspondence, show structure preserved
Mathematical dictionary served
Every time two worlds align
Galois principle divine

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