# Euler's theorem

From Groupprops

*This article gives the statement, and proof, of a particular subgroup in a group being conjugate-dense: in other words, every element of the group is conjugate to some element of the subgroup*

## Statement

Euler's theorem is any of the following equivalent statements:

- For any element of , there is an axis such that that element can be viewed as rotation about that axis
- Every element of is conjugate to an element of (where is embedded as -matrices)
- is a conjugate-dense subgroup in