Finite simple group of order two

Its pretty obvious that these words have something to do with Maths (or Math, depending on the English you prefer). I have no idea what these terms mean. Finite - ok, simple - I know the meaning, group - hmm, order - huh.. Anyway, its interesting that such a uber geeky expression "Finite simple group of order two" has been creatively composed into a song(and sung well too), that even if you don't come from a Maths background, you can very well appreciate the same. When you watch this song, you will know the different meanings of 'One to one'' and expressions such as 'I am getting "tensor" everyday' and "When we first met, we were connected(graphs)" to name a few. How about, "And by corollary, this shows you and I to be, purely inseparable...QED". Watch the video if you dig more of these 'math nothings'(I switched english) here.

Lyrics to the song(borrowed from here):

The path of love is never smooth
But mine's continuous for you
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.