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The set of all nonsingular Affine Transformations of a Translation in Space constitutes a Group known as the affine group. The affine group contains the full linear group and the group of Translations as Subgroups.
See also Affine Complex Plane, Affine Connection, Affine Equation, Affine Geometry, Affine Hull, Affine Plane, Affine Space, Affine Transformation, Affinity
References
Birkhoff, G. and Mac Lane, S. A Survey of Modern Algebra, 3rd ed. New York: Macmillan,
p. 237, 1965.