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 : )
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...
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...
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Homework Statement
Problem: Let A\subsetS be a subset of a regular surface S. Prove that A is a regular surface...