What are 3 applications of group theory?

Question

kinggeorge · Answer

Are we talking applications in the real world, or applications in other parts of math?

swissgirl · Answer

I am assuming other parts of math

kinggeorge · Answer

Well, the big one in my mind is number theory. Modular addition/multiplication makes a very good group. For example, using Lagrange's theorem allows us to consider Fermat's Little Theorem as a corollary.

kinggeorge · Answer

It can also be used for finding the symmetries of a solid object such as a square or a cube (probably a hypercube as well, but I'm not sure how).

swissgirl · Answer

yaaaaa and one moreeeeee lol

kinggeorge · Answer

Hmmm.....

kinggeorge · Answer

You can use groups/rings to "create" the complex numbers. $\mathbb{C}$ is just the algebraic closure of $\mathbb{Q}$. 

You can also look at permutations and the set of symmetric functions with groups/rings as well.

swissgirl · Answer

okkkk will research a lil bit abt that

swissgirl · Answer

Thhannksss :)

kinggeorge · Answer

I do know that group theory is an excellent way to model particle physics in the standard model. I'm not sure how or why, but that's what I've heard.

swissgirl · Answer

Ill do a lil research gotta post by 1 am

anonymous · Answer

apparently it is used in chemistry too
something to do with permutations and molecules
looks like a job for google

swissgirl · Answer

yaaa guess sooooooooooooooooooooooooooooooooooooooooooooooooooo