group (mathematics)

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.Many of the structures investigated in mathematics turn out to be groups. These include familiar number systems, such as the integers, the rational numbers, the real numbers, and the complex numbers under addition, as well as the non-zero rationals, reals, and complex numbers, under multiplication. Other important examples are the group of non-singular matrices under multiplication and the group of invertible functions under composition. Group theory allows for the properties of such structures to be investigated in a general setting.
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