Yes Islamists live in 'the west', however that does not lead to the conceit that they are all extremists.
Okay I do not adhere to the conceit of idiology being the basis of society. There have and are extremsts through any cult you wish to choose across human history.
The use of the term 'extermination' has been the justification for too long in the homocene epoch to clarify political desire and should be seen as a faulty conceit...look at how it was once used in York (England) for example.
Islamist: an advocate or supporter of the arcane text contained within the tome known as The Koran.
The Koran: An arabic derivion of the Semitic/post Martu text known as the Tora adopting aspects of the Coptic prose originating from extant north African (Egypt/Sumer/Sudan) oral histories with the pre Saladin concepts.
No I have no idea what an 'Islamist' is..."is" an assertion without definition.
You were not very specific in your post about what to exterminate.
At first I thought you just want to murder everyone that's a muslim from the planet and then share the empty land between the European nations and prehaps the US. As no one whould just let empty land to be unoccupied and it's resources be unused.
But I read your other posts seeing that your issue is more with the islamists which are part of ISIS which I am with the removal off.