I've been looking at new cars. I thought I should apply algebraic mathematical reasoning to the task, so here is a short glossary for mathematicians:
Automorphism: The process of exchanging your old car and bank account for a new one.
Inner Automorphism: The process of turning oneself inside out in order to get into the new car.
Group: The collection of people you wish to transport.
Subgroup: The subset of the group that will actually fit into the car.
Cyclic subgroup: Those who didn't fit in the car and so must peddle.
Ideal: The car you could have bought for a lot more money.
Abelian Group: Those who need a car because they commute.
Left Coset: Where the commanding officer/driver sets in the US.
Right Coset: Analogous location in UK & a few other benighted realms.
Isomorphism: The car that's just as good as the old car except for costing a lot more.
Homomorphism: This term is deprecated as possibly offensive to some.
Lagrange's Theorem: A notorious mountain in France often featured in the Tour de France. Cannot be climbed by the numerically weak.
Representation Theory: The lies used by the car salesman in order to suck you in.
Finite Dimensional Representation: The sticker price.
Infinite Dimensional Representation: How much you will actually pay.
Galois Theory: Explains why the mechanic cannot get to the root of your car's mechanical problems even by resorting to radical measures.