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## Main Question or Discussion Point

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?