| 1. | any collection or assemblage of persons or things; cluster; aggregation: a group of protesters; a remarkable group of paintings. |
| 2. | a number of persons or things ranged or considered together as being related in some way. |
| 3. | Also called radical. Chemistry. two or more atoms specifically arranged, as the hydroxyl group, –OH. Compare free radical. |
| 4. | Linguistics.
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| 5. | Geology. a division of stratified rocks comprising two or more formations. |
| 6. | Military.
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| 7. | Music. a section of an orchestra comprising the instruments of the same class. |
| 8. | Art. a number of figures or objects shown in an arrangement together. |
| 9. | Mathematics. an algebraic system that is closed under an associative operation, as multiplication or addition, and in which there is an identity element that, on operating on another element, leaves the second element unchanged, and in which each element has corresponding to it a unique element that, on operating on the first, results in the identity element. |
| 10. | Grammar (chiefly British ). a phrase: nominal group; verbal group. |
| 11. | to place or associate together in a group, as with others. |
| 12. | to arrange in or form into a group or groups. |
| 13. | to form a group. |
| 14. | to be part of a group. |

group (grōōp) n.
v. grouped, group·ing, groups v. tr. To place or arrange in a group: grouped the children according to height. v. intr. To belong to or form a group: The soldiers began to group on the hillside. [French groupe, from Italian gruppo, probably of Germanic origin.] Usage Note: Group as a collective noun can be followed by a singular or plural verb. It takes a singular verb when the persons or things that make up the group are considered collectively: The dance group is ready for rehearsal. Group takes a plural verb when the persons or things that constitute it are considered individually: The group were divided in their sympathies. See Usage Note at collective noun. |
group (gr&oomacr;p)
n.
An assemblage of persons or objects gathered or located together; an aggregation.
A class or collection of related objects or entities.
Two or more atoms that behave or that are regarded as behaving as a single chemical unit.
To place or arrange in a group.
To belong to or form a group.
group
A group G is a non-empty set upon which a binary operator * is defined with the following properties for all a,b,c in G:
Closure: G is closed under *, a*b in G Associative: * is associative on G, (a*b)*c = a*(b*c) Identity: There is an identity element e such that a*e = e*a = a. Inverse: Every element has a unique inverse a' such that a * a' = a' * a = e. The inverse is usually written with a superscript -1.
(1998-10-03)