# Math Help - Abstract Algebra

1. ## 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?

2. Originally Posted by GreenandGold
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.