To what extent should bullying students be punished?

You are bullying in the school set up,according to me,it is never welcome.It should taken up and thorough investigations made as to its nature,why it happened,where and the parents notified if child doesn't heed to initial warning.I had a child who was a bully and uncontrollable in the school l teach.I sought the School Manager's help and we observed him closely.She(the Manager) alerted the parents of his unbecoming behaviour.They adamantly refused,saying their child was so disciplined and focussed.They later transferred him as a protest.Unfortunately,to this day he is moving schools because he is more or less incompatible with rules and an ally to bullying others.

This really depends on several factors

1. Where the bullying act happened ?
2. Who committed the bullying act ?  when ? where and how ?
3. What was the impact of the bullying act  and the damages caused by it ?

Hope this is of help

If you have more specifics, let us discuss the details

Enough to ensure that they never bully again, whatever it takes to achieve that. There is no place in today's society for bullying in any shape, form or size and they should be made well aware of that.