Editing Multiplicative group (section)

{{Short description|Mathematical structure with multiplication as its operation}}
{{Group theory sidebar |Basics}}

In [[mathematics]] and [[group theory]], the term '''multiplicative group''' refers to one of the following concepts:

*the '''[[group (mathematics)|group]] under multiplication''' of the [[invertible]] elements of a [[field (mathematics)|field]],<ref>See Hazewinkel et al. (2004), p. 2.</ref> [[ring (mathematics)|ring]], or other structure for which one of its operations is referred to as multiplication. In the case of a field ''F'', the group is {{nowrap|(''F'' ∖ {0}, •)}}, where 0 refers to the [[zero element]] of ''F'' and the [[binary operation]] • is the field [[multiplication]],
*the [[algebraic torus]] GL(1).{{clarify|reason=this is not defined in this article nor in the linked article|date=March 2015}}