What is the IUPAC name of the following compound?
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Start by looking for the longest continuous carbon chain. That's 8 carbons giving you the oct-.
On that chain, theres an alkene at the 5 position, and an amide at the end, giving the 5-enamide. You might also write this as 5-en-1-amide, though it is implied.
The geometry of the alkene as being (E) always goes to the front of the string, as would any R or S declarations. In this case, (E) is unambiguous, but in cases where multiple points of geometry exist, you would define geometry or stereochemistry along with position (5R),(3E) etc.
So, thus far you have E-oct-5-enamide. You now need to describe the other group bound to nitrogen on the amide, this is an allyl group, providing you with the full name (E)-N-allyloct-5-enamide.