Editing Cyclic group (section)

===Integer and modular addition===
The set of [[integer]]s&nbsp;'''Z''', with the operation of addition, forms a group.<ref name="eom"/> It is an '''infinite cyclic group''', because all integers can be written by repeatedly adding or subtracting the single number&nbsp;1. In this group, 1 and −1 are the only generators. Every infinite cyclic group is isomorphic to&nbsp;'''Z'''.

For every positive integer&nbsp;''n'', the set of integers [[modular arithmetic|modulo]]&nbsp;''n'', again with the operation of addition, forms a finite cyclic group, denoted '''Z'''/''n'''''Z'''.<ref name="eom"/>
A modular integer&nbsp;''i'' is a generator of this group if ''i'' is [[relatively prime]] to&nbsp;''n'', because these elements can generate all other elements of the group through integer addition.
(The number of such generators is ''φ''(''n''), where ''φ'' is the [[Euler totient function]].)
Every finite cyclic group ''G'' is isomorphic to '''Z'''/''n'''''Z''', where ''n'' = {{abs|''G''}} is the order of the group.

The addition operations on integers and modular integers, used to define the cyclic groups, are the addition operations of [[commutative ring]]s, also denoted '''Z''' and '''Z'''/''n'''''Z''' or '''Z'''/(''n''). If ''p'' is a [[prime number|prime]], then '''Z'''/''p'''Z''''' is a [[finite field]], and is usually denoted '''F'''<sub>''p''</sub> or GF(''p'') for Galois field.