Editing Multiplicative group (section)

== Examples ==
*The [[multiplicative group of integers modulo n|multiplicative group of integers modulo ''n'']] is the group under multiplication of the invertible elements of <math>\mathbb{Z}/n\mathbb{Z}</math>.  When ''n'' is not prime, there are elements other than zero that are not invertible.
* The multiplicative group of [[positive real numbers]] <math>\mathbb{R}^+</math> is an [[abelian group]] with 1 its [[identity element]]. The [[logarithm]] is a [[group isomorphism]] of this group to the [[additive group]] of real numbers, <math>\mathbb{R}</math>.
* The multiplicative group of a field <math>F</math> is the set of all nonzero elements: <math>F^\times = F -\{0\}</math>, under the multiplication operation. If <math>F</math> is [[finite field|finite]] of order ''q'' (for example ''q'' = ''p'' a prime, and <math>F = \mathbb F_p=\mathbb Z/p\mathbb Z</math>), then the [[finite field#Multiplicative_structure|multiplicative group]] is cyclic: <math>F^\times \cong C_{q-1}</math>.