One of these is C, the cyclic group with three elements.

It forms a cyclic group with 2 as one choice of generator.

Cyclic groups C, where n is not divisible by eight.

This result has been called the fundamental theorem of cyclic groups.

The notation refers to the cyclic group of order n.

A primary cyclic group is one whose order is a power of a prime.

The indecomposable objects are the cyclic groups of prime power order.

This is a part of representation theory of cyclic groups.

This can be done with any finite cyclic group.

Some cyclic groups have an infinite number of elements.

A similar space for an isosceles triangle is the cyclic group of order 2, C.

Unlike the infinite cyclic group, it is not even countable.

As these two prototypes are both abelian, so is any cyclic group.

Cyclic groups of small order especially arise in various ways, for instance:

All cyclic groups of a given order are isomorphic to .

So an absolute presentation for the cyclic group of order 8 is:

It is always cyclic or the product of two cyclic groups.

This is a cyclic group of order n.

However this group is the direct product of two infinite cyclic groups and so has solvable word problem.

The result is that the word problem, here for the cyclic group of order three, is solvable.

The girth of a cyclic group equals its order.

The structure of G is an infinite sum of cyclic groups.

The protocol is defined for a cyclic group of order with generator .

Consider a cyclic group G of order q.

The group 'G' is cyclic group, and so are its subgroups.