Notes on Group Theory III

In general, groups are determined by the help of an operation, called "composition" by which to every ordered pair a, b of elements a third element ab = c is attached. There is however a second mode of representing group theory, where instead of an operation operating on a pair of elements, a 3-term relation is introduced. E.g. the equation abc = 1 can be replaced by the statement that the relation R(a, b, c) holds.