(to the tune of "Looking Out My Back Door" by CCR)
Just extended up my field, non-canonically, I feel
Got to consider Galois K over F
Generators teeming, normalizers fig’ring
Doo, doo, doo, groups acting on my sets
With a transitive free action
The quotient’s smooth - I’m laughing
Look at all the coverin’ spaces mapping down to here
A cone point and a mirror, reflecting just like snooker
Doo, doo, doo, groups acting my sets
Euclidean isometries are acting on R^n
Won’t you take a glide reflection in my plane
Doo doo doo
Translations and rotations, preserving orientation
Doo, doo, doo, groups acting on my sets
Möbius transformations act on the Riemann sphere
Some of them preserve the upper half plane
they do
Dilations and inversions, conformal non-perversions
Doo, doo, doo, groups acting on my sets
Forward-time dynamics now, a limit cycle - oh wow
Look at each trajectory accumulating here
To infinity tomorrow? In finite time no sorrows.
Doo, doo, doo, groups acting on my sets.