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?.

group theory

There are operations that are not rotations?

Add your own answers!

Related Questions

Prove if infinite product of $f(x)$ is $0$ then so is infinite product of $f(xvarphi)$

Term for “field-like” algebraic object with infinitely-many “scaled” multiplication” operations parameterized by its elements?

Intersecting diameter and chord

Tic-tac-toe with one mark type

Naming of contravariant vector field and covariant vector field

Does convergence imply uniform convergence in this example?

Normal endomorphism on a group

Hypercube traversal algorithm

How do the Christoffel symbols on an abstract manifold relate to those on submanifolds?

Rootspaces are $mathop{ad}$ nilpotent

extension of a function to a differentiable function

Is $-2^2$ equal to $-4$, or to $4$?

Proof of $sum_{k=0}^m binom{n}{k}(-1)^k = (-1)^m binom{n-1}{m}$ for $n > m geq 0$

Solving $0=sum_{T=0}^{L}(2u^2A-2Ou)$ for $O$

The meaning of definition written in the form … is…

Challenging problem: Find $a$ where $int_0^infty frac{cos(ax)ln(1+x^2)}{sqrt{1+x^2}}dx=0$.

Sheldon Axler Measure Integration Real Analysis Section 2B Exercise 11

fibre of a scheme of finite type over a field being quasi-compact

What are the solutions of $frac{pi^e}{x-e}+frac{e^pi}{x-pi}+frac{pi^pi+e^e}{x-pi-e}=0$?

Equality of an Inequality

Ask a Question