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Abstract Algebra

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humph:
Hah, I remember this question. It's quite obvious if you don't overcomplicate it: just take and any subgroup (as is abelian, every subgroup is normal in ).

/0:
Oh right, yeah does work. I was trying to do it for for some reason :(, but I think (at least) most subgroups of are isomorphic to that, because for all you can take , , but for you don't get a surjective map from . Bah, in the end I said no example was possible lol. If only I tried the most obvious quotient group

/0:
When R is a commutative ring, and N is the set of nilpotents elements of R, prove that the only nilpotent element of R/N is zero.







But if how can I show that ?

After all, in ,

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