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Thread: elements in a finite group with different finite order

  1. #1
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    elements in a finite group with different finite order

    Let $\displaystyle a, b$ in a finite group $\displaystyle G$ such that $\displaystyle a \neq b$.
    I know $\displaystyle |a|$ and $\displaystyle |b|$ divides $\displaystyle |G|$.
    Is there any condition for $\displaystyle |a| \neq |b|$, other than looking at the conjugacy classes?
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  2. #2
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    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.
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