301.3E Centralizer of an Element of a Group

The centralizer of an element a in a group G is the set of all elements of G that commute with a. Definition, example, and how to keep abelian, center, and centralizer definitions straight.

[CraaaabPeople]

Well done! Made the concepts of center and centralizer very intuitive.

[PunmasterSTP]

Centralizer? More like "Cool video; now we're wiser!"

[julimate]

Your explanation was great but I wasn't able to find the link to the dihedral group explorer you used in this video :c

[ali]

Greetings. As always, thank you for excellent video lectures. Question?: 9:50-9:55
If centralizers are subgroups, as you said they are, then the smallest non trivial centralizer has two elements, e and the second element, provided the second elements is its own inverse. If the element beside e is not its own inverse, then the smallest centralizer should have three elements. Am I correct?

[NeillClift]

When you say the centralizer is the largest set of elements that commute I start thinking there are multiple sets and you pick the largest. My thinking is that you are really saying that its the set of all g that commute with a.