# Group

- A set and an operation on the set that satisfy (eg. integers, +)

- Associativity: for all x, y, z in the set: (x op y) op z = x op (y op z)
- All results of the operation on elements of the set are also part of the set
- there exists a neutral element such that for all x in the set, x (op) neutral element == neutral element (op) x = x
- For all x in the set, there exists an inverse y such that x (op) y == neutral element

- Associativity: for all x, y, z in the set: (x op y) op z = x op (y op z)