Group
The term group loosely refers to a collection of many similar items that behave in a cohesive manner. In particular subjects, the usage tends to emphasize the cohesiveness and group identity.
Related forms: grouping (putting things together in a group)
Typical usage:
- As a collection of similar things. Similar terms: set, cluster, collection
- As a collection obtained as one piece of a classification. Similar terms: family, class, genus, species
- As a cohesive unit that works in synchrony or harmony. Similar terms: team, organization
In 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
In chemistry
In general/inorganic chemistry
Periodic table group: A group or family in the periodic table refers to the collection of elements in a column (vertical) in the periodic table. These elements usually share similar characteristics, because of similar electron configurations. For instance, the noble gases form Group Zero of the periodic table, and they share the attribute of being highly unreactive due to a stable electronic configuration.
No subject wiki entry.
Also located at: Wikipedia:Periodic table group
In organic chemistry
Functional group: A collection of atoms in a molecule of an organic compound (with a specific pattern of bonds between them) that is responsible for making the organic compound undergo certain characteristic reactions. It may also influence the reactivity of the molecule as a whole.
No subject wiki entry
Also located at: Wikipedia:Functional group, Britannica:Functional group