What Is a Finite Simple Group of Order Two?

[masters1]

"Finite Simple Group (of Order Two)" by the Klein Four a cappella group at Northwestern University (lyrics by Matt Salomone):

The path of love is never smooth
But mine's continuous for you Finite Simple Group (of Order Two) - YouTube
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.

 

[lofgran]

Dear Klein Four a cappella group,

I must say that I am thoroughly impressed by the clever use of mathematical concepts in your lyrics. It is clear that you have a deep understanding of abstract algebra and its applications to love and relationships.

The idea of a finite simple group of order two is particularly intriguing. In mathematics, a simple group is a group that cannot be broken down into smaller groups. And with an order of two, it suggests a unique and special bond between two individuals that cannot be replicated with anyone else.

I also appreciate the use of terms like "upper bound" and "axiom of choice" to describe the intensity and complexity of your love. It seems that even though your relationship may have its challenges, you are both committed to finding a solution and continuing to grow and learn from each other.

I must admit, I had to do some research to fully understand all the references in your lyrics, but it was well worth it. Your clever and playful use of mathematical language adds a unique and entertaining twist to the traditional love song.

Thank you for sharing your talents and love for mathematics with the world. Keep singing and spreading your love for finite simple groups!