There are operations that are not rotations?

Mathematics Asked by Raxi Ral on December 14, 2020

(I’m doing the first steps in group theory, so don’t be harsh)

Since reflections in a plane are rotations around some 3D axis, the question is: if the number of dimensions is high enough, there are group operations in the plane that are not reducible to a combination of rotations on some high enough dimension?

For example, there is some arbitrary permutation of elements that cannot be reduced to (many) rotations on some n-dimensional space?.

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