May, Might and Must

One of the meanings of may and might is to be allowed to. 

e.g. The members of the organization agree that I may join it.
 

The members of the organization agreed that I might  join  it. 

The auxiliary must is a stronger form of may and might. One of the meanings of must is to be obliged to or to have to.
e.g. You must provide proper identification in order to cash a check.
They must work harder if they are to succeed.


It should be noted that the meaning of must not is to be obliged not to.
e.g. You must not leave.
He must not speak.
The first example has the meaning, You must stay. The second example has the meaning, He must be silent