- #1
Wledig
- 69
- 1
So I'm just beginning to study abstract algebra and I'm not sure I grasp the definition of a quotient group, I believe it probably has to do with the book providing little to no examples. In trying to come up with my own examples, I imagined the following:
Consider the Klein four group, if we take the subgroup (e,a) and apply the defintion we ought to get
e(e,a) = (e,a)
a(e,a) = (a,e)
b(e,a) = (b,c)
c(e,a) = (c,b)
So K4/(e,a) = {(e,a), (b,c)}. Is that correct? Does the order the elements appear matter?
Consider the Klein four group, if we take the subgroup (e,a) and apply the defintion we ought to get
e(e,a) = (e,a)
a(e,a) = (a,e)
b(e,a) = (b,c)
c(e,a) = (c,b)
So K4/(e,a) = {(e,a), (b,c)}. Is that correct? Does the order the elements appear matter?