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Math Help - 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 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?
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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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