Definitions by George. W. Bush

group 

A group is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property.

(Z, +) is a group. The identity is 0, the inverse of a∈Z is −a, and addition is associative.

group by George. W. Bush May 31, 2023