AUTHORITIES.--Continuous groups: Lie and Engel, _Theorie der Transformationsgruppen_ (Leipzig, vol. i., 1888; vol. ii., 1890; vol. iii., 1893); Lie and Scheffers, _Vorlesungen uber gewohnliche Differentialgleichungen mit bekannten infinitesimalen Transformationen_ (Leipzig, 1891); _Idem, Vorlesungen uber continuierliche Gruppen_ (Leipzig, 1893); _Idem, Geometrie der Beruhrungstransformationen_ (Leipzig, 1896); Klein and Schilling, _Hohere Geometrie_, vol. ii. (lithographed) (Gottingen, 1893, for both continuous and discontinuous groups). Campbell, _Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups_ (Oxford, 1903). Discontinuous groups: Klein and Fricke, _Vorlesungen uber die Theorie der elliptischen Modulfunktionen_ (vol. i., Leipzig, 1890) (for a full discussion of the modular group); _Idem, Vorlesungen uber die Theorie der automorphen Funktionen_ (vol. i., Leipzig, 1897; vol. ii. pt. i., 1901) (for the general theory of discontinuous groups); Schoenflies, _Krystallsysteme und Krystallstruktur_ (Leipzig, 1891) (for discontinuous groups of motions); Groups of finite order: Galois, _[OE]uvres mathematiques_ (Paris, 1897, reprint); Jordan, _Traite des substitutions et des equations algebriques_ (Paris, 1870); Netto, _Substitutionentheorie und ihre Anwendung auf die Algebra_ (Leipzig, 1882; Eng. trans. by Cole, Ann Arbor, U.S.A., 1892); Klein, _Vorlesungen uber das Ikosaeder_ (Leipzig, 1884; Eng. trans. by Morrice, London, 1888); H. Vogt, _Lecons sur la resolution algebrique des equations_ (Paris, 1895); Weber, _Lehrbuch der Algebra_ (Braunschweig, vol. i., 1895; vol. ii., 1896; a second edition appeared in 1898); Burnside, _Theory of Groups of Finite Order_ (Cambridge, 1897); Bianchi, _Teoria dei gruppi di sostituzioni e delle equazioni algebriche_ (Pisa, 1899); Dickson, _Linear Groups with an Exposition of the Galois Field Theory_ (Leipzig, 1901); De Seguier, _Elements de la theorie des groupes abstraits_ (Paris, 1904), A summary with many references will be found in the _Encyklopadie der mathematischen Wissenschaften_ (Leipzig, vol. i., 1898, 1899). (W. Bu.) FOOTNOTE: [1] The word "group," which appears first in English in the sense of an assemblage of figures in an artistic design, picture, &c., is adapted from the Fr. _groupe_, which is to be referred to the Teutonic word meaning "knot," "mass," "bunch," represented in English by "crop" (q.v.). The technical mathematical sense is not older than 1870.