trippelgrupper

A trippelgrupp is a term used in mathematics, specifically in the study of abstract algebra and group theory, to refer to a group of order three. By Lagrange's theorem, any group whose order is a prime number must be cyclic. Therefore, any trippelgrupp is isomorphic to the cyclic group of order three, often denoted as C3 or Z3. This means all trippelgrupper are structurally identical.

The elements of a trippelgrupp can be represented as {e, a, a^2}, where 'e' is the identity element and 'a' is a generator element. The operation within the group is such that a^3 = e. For example, the integers modulo 3 under addition form a trippelgrupp, where the elements are {0, 1, 2} and the operation is addition modulo 3. In this case, 0 is the identity element, 1 is a generator, and 1 + 1 + 1 = 3, which is congruent to 0 modulo 3. The structure of trippelgrupper is fundamental in understanding more complex group structures.