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—groupwise, adv./groohp/, n.1. any collection or assemblage of persons or things; cluster; aggregation: a group of protesters; a remarkable group of paintings.2. a number of persons or things ranged or considered together as being related in some way.3. Also called radical. Chem. two or more atoms specifically arranged, as the hydroxyl group, -OH. Cf. free radical.4. Ling.a. (in the classification of related languages within a family) a category of a lower order than a subbranch and of a higher order than a subgroup: the Low German group of West Germanic languages.b. any grouping of languages, whether it is made on the basis of geography, genetic relationship, or something else.5. Geol. a division of stratified rocks comprising two or more formations.6. Mil.a. Army. a flexible administrative and tactical unit consisting of two or more battalions and a headquarters.b. Air Force. an administrative and operational unit subordinate to a wing, usually composed of two or more squadrons.7. Music. a section of an orchestra comprising the instruments of the same class.8. Art. a number of figures or objects shown in an arrangement together.9. Math. an algebraic system that is closed under an associative operation, as multiplication or addition, and in which there is an identity element that, on operating on another element, leaves the second element unchanged, and in which each element has corresponding to it a unique element that, on operating on the first, results in the identity element.10. Gram. Chiefly Brit. a phrase: nominal group; verbal group.v.t.11. to place or associate together in a group, as with others.12. to arrange in or form into a group or groups.v.i.13. to form a group.14. to be part of a group.[1665-75; < F groupe < It gruppo Gmc]Syn. 12. order, organize, classify, combine.Usage. 1, 2. See collective noun.
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(as used in expressions)Joint Photographic Experts GroupUnion GroupAltria Group Inc.American Volunteer GroupSeven Group of* * *
in mathematics, set that has a multiplication that is associative [a(bc) = (ab)c for any a, b, c] and that has an identity element and inverses for all elements of the set. Systems obeying the group laws first appeared in 1770 in Joseph-Louis Lagrange's studies of permutations of roots of equations; however, the word group was first attached to a system of permutations by Évariste Galois (Galois, Évariste) in 1831. It was Heinrich Weber, in 1882, who first gave a purely axiomatic description of a group independently of the nature of its elements. Today, groups are fundamental entities in abstract algebra and are of considerable importance in geometry, physics, and chemistry.in chemistry, a set of chemical elements in the same vertical column of the periodic table. The elements in a group have similarities in the electronic configuration of their atoms, and thus they exhibit somewhat related physical and chemical properties.The periodic table has eight main groups: 1, 2, 13, 14, 15, 16, 17, and 18 (previously numbered Ia, IIa, IIIa, IVa, Va, VIa, VIIa, and 0, respectively). Each group consists of elements that have similar electronic structures characterized by completely filled inner electron shells and by a number of electrons in their outermost shells equal to the group number. Ten other groups—3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 (previously numbered IIIb, IVb, Vb, VIb, VIIb, VIII, Ib, and IIb, with group VIII comprising groups 8, 9, and 10)—found only in Periods 4 to 7 of the table, are composed of elements of the transition series. With these elements the number of outermost electrons does not necessarily correspond to the group number.* * *
Universalium. 2010.
