Running GitLab CE, Omnibus installer, version 12.9.1-ee (0ebcf602332). Group owners are unable to add users to their groups. The “Members” page is completely lacking the “Invite member” section. Compare this to the page I see, when logged in as an Administrator, which DOES show the Invite Member section. Is this an Enterprise Edition, or paid option, only?
If you have LDAP enabled, and “Lock memberships to LDAP synchronization” setting enabled too, then only administrator can manage memberships of any group.
See documentation for more details on this setting.
I hope this will help.