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. A group is a set of processes that cooperate in carrying out a common task. 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.