In literature, there are many different forms of group authentication in conference key establishment protocols. The agents participating in a group need to authenticate each other in order to become assure that every agents that has access to the group key is an eligible member. In this paper, we informally classify different group authentication schemes, based on how the agents authenticate each other and provide examples of each class. We then improve one of the well-known key establishment protocol to an authenticated version according so that it meets one of our notions of group authentication.