This is not really a homework questions, rather a concept based one. I am studying from Fraleigh's ''Intro to abstract algebra'' and in chapter 15 it states, that for a group G and normal non-trivial subgroup of N of G, the factor group G/N will be smaller than G. I am not sure how he counts the change in size of the group.(adsbygoogle = window.adsbygoogle || []).push({});

For instance(ex from wiki), if we take G=Z_{6}and it's normal subgroup N={0,3} we get G/N to be { {0, 3}, {1, 4}, {2, 5} } (i.e. all the cosets, which partition the whole of G). Or do we take each coset as a different element in G/N ?

That is a={0,3}, b= {1,4}, c={2,5} so that |G/N| = 3 ?

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# Homework Help: Is a factor group by a non-trivial normal subgroup is always smaller than the group ?

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