## Finite Simple Group (of order most excruciatingly 1)

Saturday, March 08, 2008 by Mohan K.V

And right when I thought it was just another dreary day spent deciding between red pills and blue pills (with not a shade of any other color :-( Life in Magenta sucks), along came this wee song that had me completely in splits! It's by this band The Klein Four Group, and all the members are math grad students at Northwestern University. The song's called "Finite Simple Group (of Order Two)", and it makes for a lovely, lovely tune even if you're not interested in Group Theory in the least :-) Thanks a ton, Harshal!

And here are the lyrics:

Finite Simple Group (of Order Two)

The Klein Four Group

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

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.