[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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