What's your favorite algebraic structure /sci/?

Addition

>>7808218
Addition isn't a structure, and as an operation it is ambiguous

>>7808205
GL(3,R)

Geometric algebra. The way you've been taught vectors is retarded.

your mum

>>7808205
Groups never disappoint

>>7808205
accidentally, your pic. frames have been useful a number of times.

but I think I really miss groups. specifically, A5, S5, and the icosahedral group. they give a nice set of examples of exchanges between representation theory, geometry, and galois theory.

>>7808205
The ADE diagrams, for some reason they pop up in almost all fields of math. You can classify the simple lie algebras with them (if you use the B, C and F diagrams as well) and I just finished a course on singularity theory where they where used to classify all simple singularities. Apparently there are more examples. There doesn't seem to be any direct connection between the use cases so it seems the construction is just reaally fundamental to math.

The automosphism group of Z/10Z