From WordNet (r) 2.0 (August 2003) [wn]:
group
n 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}]
v 1: arrange into a group or groups; "Can you group these shapes
together?"
2: form a group or group together [syn: aggroup]
From The Collaborative International Dictionary of English v.0.48 [gcide]:
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.
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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.
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From The Collaborative International Dictionary of English v.0.48 [gcide]:
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.
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The difficulty lies in drawing and disposing, or, as
the painters term it, in grouping such a multitude of
different objects. --Prior.
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Grouped columns (Arch.), three or more columns placed upon
the same pedestal.
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From The Collaborative International Dictionary of English v.0.48 [gcide]:
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.
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The residue of them will I deliver to the sword.
--Jer. xv. 9.
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If church power had then prevailed over its victims,
not a residue of English liberty would have been
saved. --I. Taylor.
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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.
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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.
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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.
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Syn: Rest; remainder; remnant; balance; residuum; remains;
leavings; relics.
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From The Free On-line Dictionary of Computing (19 Sep 2003) [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)