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1690s, originally an art criticism term, "assemblage of figures or objects in a painting or design," from French groupe "cluster, group" (17c.), from Italian gruppo "group, knot," perhaps ultimately from Proto-Germanic *kruppaz "round mass, lump," and related to crop. Extended to "any assemblage" by 1736. Meaning "pop music combo" is from 1958.
1718 (transitive), 1801 (intransitive), from group (n.). Related: Grouped; grouping.
An assemblage of persons or objects gathered or located together; an aggregation.
A class or collection of related objects or entities.
Two or more atoms that behave or that are regarded as behaving as a single chemical unit.
To place or arrange in a group.
To belong to or form a 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.