Can an active directory group indirectly include itself in a cycle?
Directly: No, an error is returned that A group cannot be a member of itself
Indirectly: There is nothing preventing this from happening in Active Directory, and is known as Circular Group Nesting.
I have a different experience. If you use the Active Directory Users and Computers and do a right-click on a group then select "Add to a Group", you can enter the name of the group and the add succeeds, effectively making a group a member of itself.