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transformation group


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A group with elements that are transformations with the binary operation of composition of transformations. For example, the set of rotations about a fixed point form a transformation group, but the set of reflections in axes through a fixed point do not, as the set is not closed under composition. For example, successive reflections in lines at right angles to one another is equivalent to a half-turn about the point of intersection of the axes of reflection.

Subjects: Mathematics.


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