There also are groups known not to have generic polynomials, such as the cyclic group of order 8.
In general, let G be a finite cyclic group with n elements.
The indecomposable objects are the cyclic groups of prime power order.
All cyclic groups of a given order are isomorphic to .
The notation refers to the cyclic group of order n.
It forms a cyclic group with 2 as one choice of generator.
This can be done with any finite cyclic group.
This is a part of representation theory of cyclic groups.
A primary cyclic group is one whose order is a power of a prime.
All other subgroups of 2T are cyclic groups generated by the various elements, with orders 3, 4, and 6.