We have SharePoint Owners group who will need to create folders on a particular document library and SharePoint Members group who should not be allowed to create folders.
Is there a way to accomplish this?
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You could create an "ItemAdding" event receiver to check to see if the user is from a particular sharepoint group and display an appropriate message accordingly.
Here is an article that should give you a general idea on how to go about it.
A solution I've used in the past is creating a new content type based on the Folder content type, and restricting who can use it, then going to the list setting and disabling folder creation. After that you can use any number of methods to control who can create the new custom folder. This also gives you much greater control over folders created this way, since you can add metadata to them and get creative with view and alert filters.
Hope that helps!