Can an element of a quotient group G/N in an isomorphism f:G/N--H map back onto itself if it does not have a corresponding element in H? The example I am looking at is the quotient group of the group of symmetries of an n-gon, G, where n is an even number and N equal to the normal subgroup containing the identity and a 180 rotation. H represents another n-gon with an even n, but is less than the order of G.(adsbygoogle = window.adsbygoogle || []).push({});

I have found that the quotient group G/N contains every permutation in G (which I think is incorrect) because for f to be an isomorphism, G contains rotations that don't map to H.

What's going on here?

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# Mapping Question

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