Group (mathematics)

Closure: If a and b are integers then a + b is an integer.
Associativity: If a , b , and c are integers, then ( a + b ) + c = a + ( b + c ).
Identity element: 0 is an integer and for any integer a , 0 + a = a + 0 = a .
Inverse elements: If a is an integer, then the integer − a satisfies the inverse rules: a + (− a ) = (− a ) + a = 0.

In abstract algebra, a group is a set with a binary operation that satisfies certain axioms, detailed below. For example, the set of integers with addition is a group. The branch of mathematics which studies groups is called group theory.