# Group (mathematics)

**Group**: A set equipped with a binary operation (called multiplication) that is associative, has an identity element (also known as neutral element or multiplicative unit) and has left and right inverses for every element.

Groups occur throughout mathematics, and are the underlying structures for rings, fields, vector spaces, modules, function spaces, and other structures that arise naturally in algebra, analysis and topology.

Related terms: subgroup, quotient group, homomorphism of groups, normal subgroup

Primary subject wiki entry: Groupprops:Group

Survey articles related to this subject wiki entry: Groupprops:History of groups, Groupprops:Understanding the definition of a group, Groupprops:Verifying the group axioms, Groupprops:Manipulating equations in groups, Groupprops:Groups as symmetry

Guided tours related to this subject wiki entry: Groupprops:Groupprops:Guided tour for beginners

Categories related to group: Groupprops:Category:Variations of group lists variations of the notion of group, Groupprops:Category:Particular groups lists some particular groups (upto isomorphism), Groupprops:Category:Group properties lists properties that can be evaluated for a group, Groupprops:Category:Views of the collection of groups gives different viewpoints for studying the collection of all groups

Also located at: Wikipedia:Group (mathematics), Mathworld:Group, Planetmath:Group, Citizendium:Group