I have read some baby's first basic abstract algebra with some group theory. As far as I understand if we have a
- Set of any kind of mathematical object and then
- Some binary operator which makes sense for these objects and which outputs new objects.
- Follows the group axioms
Then we have a group!
So to my question, if we imagine as a set we pick a bunch of functions and as binary operator we pick convolution... Do there exist any famous such sets which with together it can create a group?