Abstract Algebra

• October 17th 2008, 09:36 AM
GreenandGold
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?
• October 17th 2008, 10:13 AM
ThePerfectHacker
Quote:

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.