group

group
    n 1: any number of entities (members) considered as a unit [syn:
         {group}, {grouping}]
    2: (chemistry) two or more atoms bound together as a single unit
       and forming part of a molecule [syn: {group}, {radical},
       {chemical group}]
    3: a set that is closed, associative, has an identity element
       and every element has an inverse [syn: {group}, {mathematical
       group}]
    v 1: arrange into a group or groups; "Can you group these shapes
         together?"
    2: form a group or group together [syn: {group}, {aggroup}]
    

Group \Group\ (gr[=oo]p), n. [F groupe, It. gruppo, groppo,
   cluster, bunch, packet, group; of G. origin: cf. G. kropf
   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.
      [1913 Webster]

   2. An assemblage of objects in a certain order or relation,
      or having some resemblance or common characteristic; as,
      groups of strata.
      [1913 Webster]

   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.
      [1913 Webster]

   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.
      [1913 Webster]
    

Group \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.
   [1913 Webster]

         The difficulty lies in drawing and disposing, or, as
         the painters term it, in grouping such a multitude of
         different objects.                       --Prior.
   [1913 Webster]

   {Grouped columns} (Arch.), three or more columns placed upon
      the same pedestal.
      [1913 Webster]
    

Residue \Res"i*due\ (r?z"?-d?), n. [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.
      [1913 Webster]

            The residue of them will I deliver to the sword.
                                                  --Jer. xv. 9.
      [1913 Webster]

            If church power had then prevailed over its victims,
            not a residue of English liberty would have been
            saved.                                --I. Taylor.
      [1913 Webster]

   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.
      [1913 Webster]

   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.
         [1913 Webster]

   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.
      [1913 Webster]

   Syn: Rest; remainder; remnant; balance; residuum; remains;
        leavings; relics.
        [1913 Webster]
    

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)
    

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