Category:Group Theory

Roughly speaking, a group is basically a dyadic operation which is associative, has an identity element and an inverse.

More formally, a group has a set of values, an closed binary operation (an operation which combines two of those values to yield one of those values), where the operation is associative (when the operation is to be performed multiple times on a sequence, it does not matter which instance of the operation is performed first), and has an identity element (which when combined with the operation and another element always yields that other element) and every element has an inverse element (when an element of the group's set of values is combined with its inverse element the result is the identity element for the group)

Addition is several examples of groups. (Here, the set of values could be integers, real numbers, complex numbers, vectors, matrices, etc.)

Permutations (of different lengths) are some more examples of groups.

There's a variety of algebraic structures which are share properties with groups.