[Verse 1]
In the realm where structure meets the dance
Four sacred laws give order its chance
Take any two and blend them tight
Closure keeps them in our sight
What you create won't drift away
Inside the family it will stay
[Chorus]
Group theory's got the magic code
Closure, inverse, identity's hold
Associativity binds the chain
Four axioms that always remain
G with dot, the perfect pair
Symmetry floating in the air
[Verse 2]
Parentheses can shift around
But the answer stays profound
A times B times C equals three
Bracket dance sets algebra free
Identity sleeps within the fold
Silent guardian, brave and bold
[Chorus]
Group theory's got the magic code
Closure, inverse, identity's hold
Associativity binds the chain
Four axioms that always remain
G with dot, the perfect pair
Symmetry floating in the air
[Bridge]
Every element finds its twin
Inverse partner dwelling within
Multiply and watch them fall
Back to one that rules them all
If the order doesn't matter
Abelian makes the pattern fatter
[Verse 3]
Integers march in perfect rows
Rationals dance where zero goes
Permutations twist and spin
Matrices battle within
Dihedral guards the polygon's face
Each reflection finds its place
[Chorus]
Group theory's got the magic code
Closure, inverse, identity's hold
Associativity binds the chain
Four axioms that always remain
G with dot, the perfect pair
Symmetry floating in the air
[Outro]
From trivial one to infinite crowd
Groups capture patterns singing loud
The language of transformation's song
Where symmetries have belonged all along