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Definitions for: Group
[n] any number of entities (members) considered as a unit
[n] a set that is closed, associative, has an identity element and every element has an inverse
[n] (chemistry) two or more atoms bound together as a single unit and forming part of a molecule
[v] arrange into a group or groups; "Can you group these shapes together?"
[v] form a group or group together
Webster (1913) Definition: Group, n. [F groupe, It. gruppo, groppo, cluster, bunch,
packet, group; of G. origin: cf. G. krepf craw, crop, tumor,
bunch. See Crop, n.]
1. A cluster, crowd, or throng; an assemblage, either of
persons or things, collected without any regular form or
arrangement; as, a group of men or of trees; a group of
isles.
2. An assemblage of objects in a certain order or relation,
or having some resemblance or common characteristic; as,
groups of strata.
3. (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.
4. (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.
Group, v. t. [imp. & p. p. Grouped; p. pr. & vb. n.
Grouping.] [Cf. F. grouper. See Group, n.]
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.
The difficulty lies in drawing and disposing, or, as
the painters term it, in grouping such a multitude of
different objects. --Prior.
Grouped columns (Arch.), three or more columns placed upon
the same pedestal.
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.
Synonyms: aggroup, chemical group, grouping, mathematical group, radical
See Also: Abelian group, accumulation, actinide, actinoid, actinon, acyl, acyl group, aggregation, alcohol group, alcohol radical, aldehyde group, aldehyde radical, alkyl, alkyl group, alkyl radical, allyl, allyl group, allyl radical, amino, amino group, arrangement, arsenic group, assemblage, assemble, association, assort, azido group, azido radical, azo group, azo radical, batch, benzoyl group, benzoyl radical, benzyl, benzyl group, benzyl radical, biological group, biotic community, bracket, brigade, building block, cacodyl, cacodyl group, cacodyl radical, carbonyl group, carboxyl, carboxyl group, chromophore, chunk, circuit, citizenry, class, classify, collection, collocate, community, commutative group, cyanide group, cyanide radical, cyano group, cyano radical, edition, electron shell, ethnic group, ethnos, foregather, forgather, gang, gang up, gather, glyceryl, halogen, hoi polloi, human beings, human race, humanity, humankind, humans, hydrazo group, hydrazo radical, hydroxyl, hydroxyl group, hydroxyl radical, ketone group, kingdom, lanthanide, lanthanoid, lanthanon, lump, man, mankind, mass, masses, meet, methylene, methylene group, methylene radical, molecule, multitude, nitrite, nitro group, people, population, propyl, propyl group, propyl radical, race, rare earth, rare-earth element, regroup, sainthood, separate, series, set, social group, sort, sort out, straggle, subgroup, subgroup, system, team, team up, unit, uranyl, uranyl group, uranyl radical, vinyl, vinyl group, vinyl radical, world
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