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• Users: IvanT
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1. Question about isomorphic direct products of groups and isomorphic factors.

Thanks a lot, that works.
2. Question about isomorphic direct products of groups and isomorphic factors.

Yeah, I still need to prove that, but at least I know that the initial statement is wrong.
3. Question about isomorphic direct products of groups and isomorphic factors.

I didn't know that, thanks a lot that solves my problem. The statement of the problem is false then. Because if RxR is isomorphic to R, then it's also isomorphic to Rx(e), and the statement of the problem would imply that R is isomorphic to the trivial group, which is false. Thanks : )
4. Question about isomorphic direct products of groups and isomorphic factors.

Homework Statement Suppose G and F are groups and GxF is isomorphic to G'xF', if G is isomorphic to G', can we conclude that F is isomorphic to F'? Homework Equations The Attempt at a Solution I'm trying to give a proof using the first isomorphism theorem (using that GxF/Gx(e) is isomorphic...
5. Problem with the change of variable theorem of integrals

Oh xD, I didn't noticed that, thanks a lot : ).
6. Problem with the change of variable theorem of integrals

Homework Statement So I came across the integral \int^{1}_{0}x\sqrt{1-x^2} and I tried to solve it in two ways using the change of variables theorem for integration, however both ways are supposed to give me the same result, but they differ in the sign and I cannot find what I am doing wrong...