- #1

Mr Davis 97

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I want to use the result for a proof I am currently doing, but I am not sure it is true.

Is it enough just to note that if ##h_1,h_2\in H##, then ##(h_1N)(h_2^{-1}N) = h_2h_2^{-1}N \in H/N##?

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- Thread starter Mr Davis 97
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- #1

Mr Davis 97

- 1,462

- 44

I want to use the result for a proof I am currently doing, but I am not sure it is true.

Is it enough just to note that if ##h_1,h_2\in H##, then ##(h_1N)(h_2^{-1}N) = h_2h_2^{-1}N \in H/N##?

- #2

- 17,263

- 17,318

No, it's wrong. The index before last has to be ##1##

I want to use the result for a proof I am currently doing, but I am not sure it is true.

Is it enough just to note that if ##h_1,h_2\in H##, then ##(h_1N)(h_2^{-1}N) = h_2h_2^{-1}N \in H/N##?

The rest is a yes.

E.g.: https://en.wikipedia.org/wiki/Isomorphism_theorems#Third_isomorphism_theorem

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