My intention is to create groups for each department in our company.  For each department there will be one or two users that will be able to edit the wordpress pages and posts for their department.  So I set up a role group with basically the same permissions as wp-author - that is, they have permissions to read pages/posts, edit pages/posts,  and delete pages/posts (published and private pages and posts, too).  I assigned the role of Page Author to the group role for their departments pages.  Yet, when I log in, I can see a list of the pages I should have access to and I can view them, but I can't edit them - it tells me I don't have the appropriate permissions to edit the page.  Yet, if I click "delete", it moves the page to Trash without any problem.

What am I doing wrong?  Why can the user delete a page but not edit it?  Any ideas of what settings I should change to get this to work?

Make sure edit_others_posts and edit_others_pages are in the role definition. Usually, "Author" means you can edit your only edit posts for which your are the stored author (per dropdown in Post Edit Form).

Also take a look at Roles > Options > RS Role Defs and sync WP role to the corresponding RS role if necessary.