Manage a Group

i've set up a ES category (let's say Alumni) and a group within called Alumni Group) which requires approval to join.

Is there a way to not show the Manage Group option inside the group page? I don't want group members to edit, unpublish or delete the group. Create discussion, announcement and album is ok. And if they do unpublish/delete are they only deleting themselves from the group or the whole group.