Students mean more than one student. Student refer's to just one student.

Michael, "No" is an adjective in your example. No student means..................................not a student No students.............................................not any students The use of "no" in your example is analogous to the use of the word "none". 'None' can be singular or plural depending on whether you want to stress the group or the individual. Ex. None of the students is to leave without permission. None of the students are to leave without permisssion. It is a good question. When I was younger, I would walk my dog and occasionally come across a sign that would read, NO DOGS ALLOWED. I asked myself the question: Well, I only have one dog with me, can I go in with just one dog? The answer is no, you can't. Languages are not always 100% logical.

Hi, at our school we say 'no students' as that takes care of the groups of students who try to leave the school grounds to go to the shops.

I think it's a subtle distinction, but "no student" sounds more strict: "not even one student may leave..." The basic difference is referring to the students as a group, or each student individually, I believe.