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From The Collaborative International Dictionary of English v.0.44 [gcide]:
Group \Group\, verb (used with an object) [imp. & p. p. {Grouped}; p. pr. & vb. n. {Grouping}.] [Cf. F. grouper. See {Group}, noun] 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.
From The Collaborative International Dictionary of English v.0.44 [gcide]:
Group \Group\ (gr[=oo]p), noun [F groupe, It. gruppo, groppo, cluster, bunch, packet, group; of G. origin: cf. G. kropf craw, crop, tumor, bunch. See {Crop}, noun]
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.
From The Collaborative International Dictionary of English v.0.44 [gcide]:
Residue \Res"i*due\ (r?z"?-d?), noun [F. r['e]sidu, L. residuum, fr. residuus that is left behind, remaining, fr. residere to remain behind. See {Reside}, and cf. {Residuum}.]
1. That which remains after a part is taken, separated, removed, or designated; remnant; remainder.
The residue of them will I deliver to the sword. --Jer. xv. 9.
If church power had then prevailed over its victims, not a residue of English liberty would have been saved. --I. Taylor.
2. (Law) That part of a testeator's estate wwhich is not disposed of in his will by particular and special legacies and devises, and which remains after payment of debts and legacies.
3. (Chem.) That which remains of a molecule after the removal of a portion of its constituents; hence, an atom or group regarded as a portion of a molecule; a {moiety} or {group}; -- used as nearly equivalent to {radical}, but in a more general sense. [1913 Webster +PJC]
Note: The term radical is sometimes restricted to groups containing carbon, the term residue and {moiety} being applied to the others.
4. (Theory of Numbers) Any positive or negative number that differs from a given number by a multiple of a given modulus; thus, if 7 is the modulus, and 9 the given number, the numbers -5, 2, 16, 23, etc., are residues.
Syn: Rest; remainder; remnant; balance; residuum; remains; leavings; relics.
From WordNet (r) 2.0 [wn]:
group
noun
1: any number of entities (members) considered as a unit [syn: {grouping}]
2: (chemistry) two or more atoms bound together as a single unit and forming part of a molecule [syn: {radical}, {chemical group}]
3: a set that is closed, associative, has an identity element and every element has an inverse [syn: {mathematical group}]
verb
1: arrange into a group or groups; "Can you group these shapes together?"
2: form a group or group together [syn: {aggroup}]
From Moby Thesaurus II by Grady Ward, 1.0 [moby-thes]:
387 Moby Thesaurus words for "group": American, Art Nouveau, Ashcan school, Barbizon, Bauhaus, Bolognese, British, Bund, Cobra, Dutch, Flemish, Fontainebleau, French, German band, Italian, Mannerist, Milanese, Modenese, Momentum, Neapolitan, New York, Paduan, Parisian, Phases, Philharmonic, Pre-Raphaelite, Raphaelite, Reflex, Restany, Rochdale cooperative, Roman, Scottish, Sienese, Spur, Suprematism, The Ten, Tuscan, Umbrian, Venetian, Washington, accumulate, accumulation, adjust, affiliation, age group, agglomerate, agglomeration, aggregate, aggregation, aggroup, alliance, alphabetize, amass, amount, analyze, appraise, arrange, array, art schools, assemblage, assemble, assembly, assess, association, assort, assortment, axis, band, batch, battalion, battery, bevy, big band, bloc, blood, body, bolt, bracket, branch, brass, brass band, brass choir, brass quintet, brass section, brasses, break down, brigade, bring together, budget, bulk, bunch, bunch together, bunch up, bundle, cabal, cadre, callithumpian band, camarilla, cartel, cast, caste, catalog, catalogue, categorize, category, cell, chain, chamber orchestra, charmed circle, chunk, church, circle, clan, class, classify, clique, closed circle, clot, club, clump, cluster, clutch, coalition, codify, cohort, collate, collect, collection, college, colligate, collocate, combination, combine, combo, common market, communion, community, company, compare, compile, complement, concert band, confederacy, confederation, congeries, conglomerate, conglomeration, congregation, consumer cooperative, contingent, cooperative, cooperative society, copse, corps, corral, coterie, council, count, couple, covey, credit union, crew, crop, crowd, cumulate, customs union, deal, denomination, desks, detachment, detail, dig up, digest, dispose, divide, division, dixieland band, dose, draw together, dredge up, drive together, eclectic, economic community, elite, elite group, enlarge, ensemble, estate, evaluate, faction, factor, federation, fellowship, file, fleet, free trade area, gamelan orchestra, gang, gather, gather in, gather together, gathering, gauge, get in, get together, gob, gradate, grade, graduate, grouping, groupment, groups, grove, guild, hassock, head, heading, heap, hunk, identify, in-group, index, ingroup, inner circle, jazz band, join, jug band, junta, junto, juxtapose, kin, knot, label, large amount, league, level, list, look-alikes, lot, lump together, machine, make up, mass, match, matching pair, measure, mess, military band, mob, mobilize, movement, muster, number, offshoot, orchestra, order, organization, organize, out-group, outfit, pack, pair, parcel, part, partner, partnership, party, passel, peer group, persuasion, phalanx, pigeonhole, pile, place, platoon, plein-air, political machine, pool, portion, position, posse, predicament, proportion, push, put together, quantity, quartet, quintet, race, ragtime band, raise, rake up, rally, range, rank, rate, rating, ration, regiment, religious order, riddle, ring, rock-and-roll group, round up, rubric, ruck, salon, schism, school, scrape together, screen, sect, sectarism, section, segment, separate, sept, series, set, set apart, sextet, shock, sieve, sift, size, skiffle band, slew, small amount, society, sort, sort out, squad, stable, station, status, steel band, stook, strain, stratum, street band, string, string band, string choir, string orchestra, string quartet, strings, subdivide, subdivision, subgroup, suborder, subordinate, suite, sum, swing band, symphony, symphony orchestra, tabulate, take up, team, thicket, thrash out, tier, title, tribe, trio, troop, troupe, trust, tuft, tussock, twins, type, union, unit, variety, version, waits, we-group, weigh, whip in, wing, winnow, wisp, woodwind, woodwind choir, woodwind quartet, woodwinds
From The Free On-line Dictionary of Computing (27 SEP 03) [foldoc]:
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)
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