The sentence fom the book is not quite correct as you can have 2 types of persistent fields (according to the spec 2.1.1; 4.3): state-field or association-field.
The difference between those two is that association field points to another entity (type is the abstract
schema type of the related entity) and the state field does not (it is just some value of type valid for persistent fields).
Example for entities "Person p" and "Account a" is:
The association fields are also part of the persistent state (driven by cascade element of the association) of an entity.
An important thing to note is JPQL is defined for an entity and its persistent state and NOT for transient or static fields.
So in this sense, the statement in EJB3 in Action is loosely defined for group by clause.