group, grouping (noun)

any number of entities (members) considered as a unit

group, radical, chemical group (noun)

(chemistry) two or more atoms bound together as a single unit and forming part of a molecule

group, mathematical group (verb)

a set that is closed, associative, has an identity element and every element has an inverse

group (verb)

arrange into a group or groups

"Can you group these shapes together?"

group, aggroup (verb)

form a group or group together

group (Noun)

A number of things or persons being in some relation to one another.

group (Noun)

A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.

group (Noun)

A (usually small) group of people who perform music together.

group (Noun)

A small number (up to about fifty) of galaxies that are near each other.

group (Noun)

A column in the periodic table of chemical elements.

group (Noun)

A functional entity consisting of certain atoms whose presence provides a certain property to a molecule, such as the methyl group.

group (Noun)

A subset of a culture or of a society.

group (Noun)

An air force formation.

group (Noun)

A collection of formations or rock strata.

group (Verb)

To put together to form a group.

group (Verb)

To come together to form a group.

group (Noun)

In the Unix operating system, a number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.

group (Noun)

An element of an espresso machine from which hot water pours into the portafilter.

Group

In mathematics, a group is a set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation; the addition of any two integers forms another integer. The abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way, while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics. Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged, and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincaré groups can express the physical symmetry underlying special relativity.

Group

A group is a number of persons or things that are located, gathered, or classed together.