English Dictionary

symmetry group

noun

(mathematics, geometry, algebra) A group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.

The symmetry group of a square is the set of all transformations that preserve its shape and size.

意味（1）

(mathematics, geometry, algebra) A group whose elements are all the transformations under which a given object remains invariant and whose group operation is function composition.

[The] situation is more delicate in the case of higher dimensional symmetry groups; it is not in general possible to reduce the order of an equation invariant under an r-parameter symmetry group by r using only quadratures.