Re: Request help

>
> jade1378 wrote:
> > For A an abelian group and n a positive integer
> define A^n={a^n: a in A}.
> > show (direct sum of A and B)/(direct sum of And
> B)^n is homeomorphic to the direct sum of A/A^n and
> B/B^n.
>
> There is the canonical map from A (+) B to A/A^n (+)
> B/B^n. What is
> the kernel of this map? Also, I think you mean
> isomorphic, not
> homeomorphic.
>
> Mike
>

I am sorry, it is isomorphic
If A is cyclic of order k, what is A/(A^n)
.

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