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dynamical symmetry group - translation to russian
![permute]] the tetrahedron through the positions. The twelve rotations form the '''rotation (symmetry) group''' of the figure.](https://commons.wikimedia.org/wiki/Special:FilePath/Tetrahedral group 2.svg?width=200 "permute]] the tetrahedron through the positions. The twelve rotations form the '''rotation (symmetry) group''' of the figure.")
![The [[cyclic group]] '''Z'''<sub>26</sub> underlies [[Caesar's cipher]].](https://commons.wikimedia.org/wiki/Special:FilePath/Caesar3.svg?width=200 "The [[cyclic group]] '''Z'''<sub>26</sub> underlies [[Caesar's cipher]].")
!['''C''' → '''C'''/('''Z''' + ''τ'''''Z''')}}, where ''τ'' is a parameter living in the [[upper half plane]].](https://commons.wikimedia.org/wiki/Special:FilePath/Torus.png?width=200 "'''C''' → '''C'''/('''Z''' + ''τ'''''Z''')}}, where ''τ'' is a parameter living in the [[upper half plane]].")
общая лексика
теория групп
математика
теория групп
Wikipedia
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X).
For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure.
