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.

(01 Apr 1998)

ground state, ground substance, ground tissue, ground water < Prev | Next > group, Group 3, Group 4

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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. <biology> A variously limited assemblage of animals or planta, 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. 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.

Origin: F groupe, It. Gruppo, groppo, cluster, bunch, packet, group; of G. Origin: cf. G. Krepf craw, crop, tumour, bunch. See Crop.

(01 Mar 1998)

ground substance, ground tissue, ground water, group < Prev | Next > Group 3, Group 4, group agglutination

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