Thread: elements in a finite group with different finite order

1. elements in a finite group with different finite order

Let $a, b$ in a finite group $G$ such that $a \neq b$.
I know $|a|$ and $|b|$ divides $|G|$.
Is there any condition for $|a| \neq |b|$, other than looking at the conjugacy classes?

2. Re: elements in a finite group with different finite order

For a general finite group? No, I don't know of any general conditions. If you had a specific type of group, then maybe.