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Stuck on this question, struggling to see where to start.

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- Mar 23rd 2009, 06:44 AMmath_helpGroups
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Stuck on this question, struggling to see where to start. - Mar 23rd 2009, 11:16 AMOpalg
Each element of HK is of the form hk, where $\displaystyle h\in H,\;k\in K$. But there may be more than one way of representing the same element as such a product.

So suppose that $\displaystyle h_1k_1 = h_2k_2$. Then $\displaystyle h_2^{-1}h_1 = k_2k_1^{-1} = p$ say, where $\displaystyle p\in H\cap K$ (because $\displaystyle p = h_2^{-1}h_1\in H$ and also $\displaystyle p = k_2k_1^{-1}\in K$).

Use that to count the number of ways that each element of HK can be expressed as a product of the form hk. - Mar 24th 2009, 02:55 AMHalmos Rules
- Mar 25th 2009, 11:39 AMmath_help
What about the counter-example?

- Mar 25th 2009, 11:46 AMOpalg