Groups
Groups Main article: Group (mathematics) See also: Group theory and Examples of groups Combining the above concepts gives one of the most important structures in mathematics: a group . A group is a combination of a set S and a single binary operation ∗, defined in any way you choose, but with the following properties: An identity element e exists, such that for every member a of S , e ∗ a and a ∗ e are both identical to a . Every element has an inverse: for every member a of S , there exists a member a −1 such that a ∗ a −1 and a −1 ∗ a are both identical to the identity element. The operation is associative: if a , b and c are members of S , then ( a ∗ b ) ∗ c is identical to a ∗ ( b ∗...