Let G be a finite group, H and K subgroups of G such that G=HK. Show that there exists a p-Sylow subgroup P of G such that P=(P∩H)(P∩K).(adsbygoogle = window.adsbygoogle || []).push({});

I found this proof and it is clear http://math.stackexchange.com/questions/42495/sylow-subgroups but I do not understand step 3 which is "It is clear in this situation that P=(P∩H)(P∩K)". Help.

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# Sylow of a group

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