Abelian group

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, an abelian group, also called a commutative group, is a <a href="/facts/Group_(mathematics)/IQTYqINt">group</a> in which the result of applying the <a href="/facts/Group_operation/IQTYqINt">group operation</a> to two group elements does not depend on the order in which they are written. That is, the group operation is <a href="/facts/Commutative/WaYxJLxd">commutative</a>. With addition as an operation, the <a href="/facts/Integer/PUwwrawx">integers</a> and the <a href="/facts/Real_number/R02gw5Pb">real numbers</a> form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after the Norwegian mathematician <a href="/facts/Niels_Henrik_Abel/6kMfdRkT">Niels Henrik Abel</a>.: 41 
</p><p>The concept of an abelian group underlies many fundamental <a href="/facts/Algebraic_structure/TkuXca24">algebraic structures</a>, such as <a href="/facts/Field_(mathematics)/xAjAS4ko">fields</a>, <a href="/facts/Ring_(mathematics)/JnCUXz63">rings</a>, <a href="/facts/Vector_space/M1pxMLx2">vector spaces</a>, and <a href="/facts/Algebra_over_a_field/8T8ulWJb">algebras</a>. The theory of abelian groups is generally simpler than that of their <a href="/facts/Non-abelian_group/KQYHrwJl">non-abelian</a> counterparts, and finite abelian groups are very well understood and fully classified.
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Abelian group open-in-new

Abelian group