Associations & model linking

Hi everybody!
I want to know if i'm doing things right, please!
I have 3 kind of users: admin,teacher,students, so i've created 3
different groups (for ACL).

For the users, I've made 3 separated tables: users (for login),
teachers, and students.

So:
Users $belongsTo Group
teachers $belongsTo Users
teachers $hasMany users
students $belongsTo User
students $belongsTo teacher

Ok?

Recap:
-Users: id,user,password,teachers_id,students_id,group_id
-Teachers:id, ..stuff.. , user_id
-Students:id, ..stuff.., teachers_id, user_id

Is this correct?
Thanks :)

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