Through Nintex (SharePoint 2013) is it possible to set item level permissions ?
If it's possible please tell me the approach
Yes, within a workflow you will use the Set Item Permissions action.
This workflow action allows the permissions to be changed for an item on which the workflow is running.
Select either the Current item that the workflow is running on, or one of the available lists or libraries.
If selecting a library list or library location, the Where selector will appear.
Run....Run as fast and as far as you can from Item Level Permissions. Don't do it.
Okay, now that I've warned you; yes, you can do that, and in some cases it is a true business requirement to do so, but I would caution against it.
As Andrew pointed out, there is a workflow action that can be done with this, also you have an option of modifying this when using the assign task as well.
Let us know if you need anything else.
I agree with Eric. You can use single item permissions but you will have to be very careful with it.
There is no general problem using them. There is a technical one though. SharePoint will inclute every single permission in its data queries. As you get more and more items in your list you will see decreasing performance of your list.
So if you need to use single item persmissions - and sometines you have to - you should also think about cleaning up items that you do not need anymore to free the queries from some load.
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