Dealing with students who sent email with empty body but the homework attached I am responsible for the exercises for a graduate course. The students submit their solutions via email and all of them send a normal email: greeting me and telling that the solutions file is attached then (most of them) wishing me a good weekend as the due dates are Fridays. 

One group sends me an empty email: just an attachment without any word!
I believe that this behaviour is odd, should I take an action or it is not my business?
I don't really think this is odd: they have been asked to send the assignment by email and they did.  There isn't really a need to say anything further and they didn't.  Maybe it would be slightly more courteous if they were to add a couple of words of greeting, but your job is not to be Emily Post.

If the assignments were submitted on paper, and they left their assignment in your mailbox, would you insist that they include a note wishing you a nice day?  No, that would be silly.

There isn't anything you need to do about this.