A
group is called
cyclic if it is generated by a single element.
If we are writing the group operation multiplicatively this means that
G={an : n in
Z}. (If we write it additively, as for some
abelian groups, then this means
G={na: n in
Z}).
An example of an infinite cyclic group is (Z,+) (generated by 1). A finite
cyclic group is the group of nth complex roots of unity
(generated by e2pii/n).
Two cyclic groups with the same order are isomorphic.
A standard notation for the cyclic group of order n is
Cn.