# Same order iff potentially conjugate

From Groupprops

## Contents

## Statement

### Verbal statement

The following are equivalent for two elements of a group:

- They have the same order.
- The group can be embedded in a bigger group in which the two elements are conjugate elements.

### Statement with symbols

The following are equivalent for elements :

- The order of equals the order of .
- There exists a group containing such that are conjugate in .

## Related facts

### Applications

- Equivalence of definitions of group in which every element is order-conjugate
- Every group is a subgroup of a group with two conjugacy classes