Isometry group

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In mathematics, the isometry group of a metric space is the set of all isometries (i.e. distance-preserving maps) from the metric space onto itself, with the function composition as group operation. Its identity element is the identity function.[1]

A single isometry group of a metric space is a subgroup of isometries; it represents in most cases a possible set of symmetries of objects/figures in the space, or functions defined on the space. See symmetry group.

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  1. ^ Burago, Dmitri; Burago, Yuri; Ivanov, Sergei (2001), A course in metric geometry, Graduate Studies in Mathematics 33, Providence, RI: American Mathematical Society, p. 75, ISBN 0-8218-2129-6, MR 1835418 .
  2. ^ Berger, Marcel (1987), Geometry. II, Universitext, Berlin: Springer-Verlag, p. 281, doi:10.1007/978-3-540-93816-3, ISBN 3-540-17015-4, MR 882916 .
  3. ^ Olver, Peter J. (1999), Classical invariant theory, London Mathematical Society Student Texts 44, Cambridge: Cambridge University Press, p. 53, doi:10.1017/CBO9780511623660, ISBN 0-521-55821-2, MR 1694364 .
  4. ^ Müller-Kirsten, Harald J. W.; Wiedemann, Armin (2010), Introduction to supersymmetry, World Scientific Lecture Notes in Physics 80 (2nd ed.), Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd., p. 22, doi:10.1142/7594, ISBN 978-981-4293-42-6, MR 2681020 .