Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Multiplicative group
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Group_theory/NfowcI5H">group theory</a>, the term multiplicative group refers to one of the following concepts: </p> <ul><li>the <a href="/facts/Group_(mathematics)/IQTYqINt">group</a> under multiplication of the <a href="/facts/Invertible/CwMygHSj">invertible</a> elements of a <a href="/facts/Field_(mathematics)/xAjAS4ko">field</a>, <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a>, or other structure for which one of its operations is referred to as multiplication. In the case of a field <i>F</i>, the group is (<i>F</i> ∖ {0}, •), where 0 refers to the <a href="/facts/Zero_element/PvH2qhxh">zero element</a> of <i>F</i> and the <a href="/facts/Binary_operation/CYtow0bz">binary operation</a> • is the field <a href="/facts/Multiplication/VtcUjpNv">multiplication</a>,</li> <li>the <a href="/facts/Algebraic_torus/U5cLv3mU">algebraic torus</a> GL(1).</li></ul>