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Math Help - Abstract Algebra

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    Abstract Algebra

    What does the order of an element in a group tell you about its centralizer? So if the order is lets say 5 what does that say about the centralizer?
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    Quote Originally Posted by GreenandGold View Post
    What does the order of an element in a group tell you about its centralizer? So if the order is lets say 5 what does that say about the centralizer?
    Remember that \left< a \right> \subseteq C(a).
    Therefore if \text{ord}(a)=5 then it means |C(a)| is a multiple of 5.
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