(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]H[/tex], [tex]K[/tex] be subgroups of a finite group [tex]G[/tex]. Consider the map, [tex]f : H \times K \rightarrow HK : (h,k)\rightarrow hk[/tex]. Describe [tex]f^{-1}(hk)[/tex] in terms of [tex]h[/tex], [tex]k[/tex] and the elements of [tex]H\cap K[/tex].

2. Relevant equations

[tex]HK = \{hk : h \in H, k \in K \}[/tex]

[tex]f^{-1}(hk)=\{ (h',k') : f(h',k')=hk \}[/tex]

3. The attempt at a solution

I should be able to get somewhere with this but I can't. Can someone give me one or two hints to start me off?

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# Homework Help: Group theory : inverse of a map.

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