## GROUP

### 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 ...

The above text is a snippet from Wikipedia: Group (mathematics)

### group

#### Noun

1. A number of things or persons being in some relation to one another.
2. A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
3. A (usually small) group of people who perform music together.
4. A small number (up to about fifty) of galaxies that are near each other.
5. A column in the periodic table of chemical elements.
6. A functional entity consisting of certain atoms whose presence provides a certain property to a molecule, such as the methyl group.
7. A subset of a culture or of a society.
8. An air force formation.
9. A collection of formations or rock strata.
10. A number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.
11. An element of an espresso machine from which hot water pours into the portafilter.
12. A number of eighth, sixteenth, etc., notes joined at the stems; sometimes rather indefinitely applied to any ornament made up of a few short notes.

#### Verb

1. To put together to form a group.
2. To come together to form a group.

The above text is a snippet from Wiktionary: group