For those of you curious, this was by far my favorite math course I ever took. Close second would be Proofs. The vast majority of the topics make intuitive sense and that makes learning this quite entertaining. Plus there are some wonderfully-named theorems.
You need to show that the center of a group is nonempty in order for the subgroup test to apply(the empty subset vacuously passes the test!). Luckily, it is pretty clear that 1 is always in the center of any group.
Like most mathematical definitions it plays well with other concepts already established (e.g. communtivity, and subgroups). Also since commutative groups are "well behaved" the center of the group tells you how "well behaved" the group is.
Idk, but I'm here because I am trying to learn about clifford algebras and geometric algebra. My intro to clifford algebras book talked about centers of groups, so here I am.
Hi, I have a small question, since G is a subgroup of G itself, so the centre of a group G is a centraliser of a subgroup, by the previous video, so it's definitely a subgroup. I think the proof here could be illustrated by the last video.
