The OG Book Inheritance module provides functionality for inheritance when assigning groups to book pages.

Books can be made to use the groups of their immediate parent or their top level parent.
The public flag can also be inherited.
Group selection can be done automatically, or users can be allowed to choose the group or override a default group selection.
The module also allows you to make groups manatory for books, so that the groups must either inherit from their parents or a selection must be made.