group

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun An assemblage of persons or objects gathered or located together; an aggregation.
• noun A set of two or more figures that make up a unit or design, as in sculpture.
• noun A number of individuals or things considered or classed together because of similarities.
• noun Linguistics A category of related languages that is less inclusive than a family.
• noun A military unit consisting of two or more battalions and a headquarters.
• noun A unit of two or more squadrons in the US Air Force, smaller than a wing.
• noun Two or more atoms behaving or regarded as behaving as a single chemical unit.
• noun A column in the periodic table of the elements.
• noun Geology A stratigraphic unit, especially a unit consisting of two or more formations deposited during a single geologic era.
• noun Mathematics A set, together with a binary associative operation, such that the set is closed under the operation, the set contains an identity element for the operation, and each element of the set has an inverse element with respect to the operation. The integers form a group under the operation of ordinary addition.
• adjective Of, relating to, constituting, or being a member of a group.
• intransitive verb To place or arrange in a group.
• intransitive verb To belong to or form a group.

from The Century Dictionary.

• To form into a group or into groups; arrange in a group or in groups; separate into groups: commonly with reference to the special mutual relation of the things grouped, to classification, or to some special design or purpose, as artistic effect.
• To fall into combination or arrangement; form a group or part of a group: used chiefly with reference to artistic effect.
• See groop.
• noun An assemblage of persons or things; a number of persons or things gathered together with or without regular interconnection or arrangement; a cluster.
• noun In the fine arts, an assemblage of figures which have some relation to one another and to the general design; a combination of several figures forming a harmonious whole.
• noun In scientific classifications, a number of individual things or persons related in some definite or classificatory way.
• noun Specifically— In zoology, any assemblage or classificatory division of animals below the kingdom and above the species: generally said of intermediate or not regularly recognized divisions, or by way of non-committal to the exact taxonomic value of the division thus indicated.
• noun In geology, a division in the geological sequence or classification of the stratified fossiliferous rocks inferior in value to a system or series. See system.
• noun In music: A short rapid figure or division, especially when sung to a single syllable.
• noun A section of an orchestra, comprising the instruments of the same class: as, the wood-wind group.
• noun In mathematics, a set of substitutions (or other operations) such that every product of operations of the set itself belongs to the set; a system of conjugate substitutions; a set of permutations resulting from performing all the substitutions of a conjugate system upon a series of elements; a set of functions produced by the n operations of a group of operations from n independent functions, called the fundamental system of the group.
• noun A group of infinitely many but discrete operations, among which infinitely small transformations occur.
• noun in mathematics, a group whose elements have each k indices, or are arranged in a matrix of k dimensions.
• noun In Capelli's extended sense, groups which can be separated each into the same number of subgroups, so that a substitution of a subgroup in the one can be so coordinated to one of the other that products shall correspond to products.
• noun In the recommendations of the International Geological Congress this term is applied, in geological classification, to stratigraphic divisions of the highest order comprising several terrains. Its equivalent term in the time scale is era.
• noun In combinatorial analysis, one of the classes into which the objects are distributed when the order of the objects in a particular class is material.
• noun In group-theory, a set of definite operations containing the operation compounded of any two of the set, and also the inverse of every operation of the set.
• noun In crystallography, a class of crystals characterized by the same degree of symmetry. Each crystalline system embraces several such groups or classes. See symmetry, where the names commonly employed in designating the more important of these groups are given.
• noun In ethnology, a number of people united together by common habits and usages.

from the GNU version of the Collaborative International Dictionary of English.

• transitive verb To form a group of; to arrange or combine in a group or in groups, often with reference to mutual relation and the best effect; to form an assemblage of.
• transitive verb (Arch.) three or more columns placed upon the same pedestal.
• noun A cluster, crowd, or throng; an assemblage, either of persons or things, collected without any regular form or arrangement.
• noun An assemblage of objects in a certain order or relation, or having some resemblance or common characteristic.
• noun (Biol.) A variously limited assemblage of animals or plants, having some resemblance, or common characteristics in form or structure. The term has different uses, and may be made to include certain species of a genus, or a whole genus, or certain genera, or even several orders.
• noun (Mus.) 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A number of things or persons being in some relation to one another.
• noun group theory A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.
• noun A (usually small) group of people who perform music together.
• noun astronomy A small number (up to about fifty) of galaxies that are near each other.
• noun chemistry A column in the periodic table of chemical elements.
• noun chemistry A functional entity consisting of certain atoms whose presence provides a certain property to a molecule, such as the methyl group.
• noun sociology A subset of a culture or of a society.
• noun military An air force formation.
• noun geology A collection of formations or rock strata.
• noun computing In the Unix operating system, a number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.