We revisit the well-known group membership problem, and show how it can be considered a special case of a simpler problem, the set membership problem. In the set membership problem, processes maintain a set whose elements are drawn from an arbitrary universe: they can request the addition or removal of elements to/from that set, and they agree on the current value of the set. Group membership corresponds to the special case where the elements of the set happen to be processes. We exploit this new way of looking at group membership to give a simple and succint specification of this problem and to outline a simple implementation approach based on the state machine paradigm. This treatment of group membership separates several issues that are often mixed in existing specifications and/or implementation of group membership. We believe that this separation of concerns greatly simplifies the understanding of this problem.