Group-based computing is becoming more and more popular when one has to design a middleware able to support reliable distributed applications. This paradigm is made of two basic services, namely, a group membership service and a group communication service. More generally, a group is a set of processes cooperating to carry out a common task (e.g., copies of a replicated server, participants in a transaction or users in a CSCW-based application). Due to the desire of new processes to join the group, to the desire of a group member to leave it, or to process crashes, the composition of a group can evolve dynamically. The set of processes that currently implements the group is called the current view of the group. This paper addresses the specification and the implementation of a primary component group membership service. "Primary component" means that the specification imposes to have a single view at any time. The paper first proposes a specification for the problem. Then it presents a protocol that implements that specification in asynchronous distributed systems equipped with failure detectors. This primary component group membership protocol is obtained as an appropriate instantiation of a general agreement framework.