Is it permissible for a teacher to say to her students: "Allah does not permit nor does He make lawful for whoever speaks during my class," and is there a sin incurred by one who speaks after this statement?

Islam urges good manners towards the teacher. The Prophet, peace and blessings be upon him, said: "He is not of us who does not respect our elders, have mercy on our young, and acknowledge the right of our scholar." Among the manners with a teacher are: not speaking excessively in their presence, not interrupting them or preempting them in speech, for the student to wait until the teacher finishes speaking, and not to converse with others while the teacher is speaking. As for mere talking, there is no sin in it unless it results in harm to the students or the female teacher.