The group membership service is probably the most important protocol layer, and also the most complex to implement. The description is based on the current (March 99) GMS layer, but work is underway to replace this layer with a new one (RpcGMS).
When a CONNECT event is received by the GMS layer, it tries to join the group. To do so, it first tries to retrieve the initial membership. If no other members can be found, it assumes it is the first member and sends a VIEW_CHANGE event up/down the stack. Otherwise, it determines the coordinator and sends a unicast message to the latter to join it to the group. The coordinator adds the new member to its local view and multicasts the new view to all GMS layers, which then in turn generate VIEW_CHANGE events up/down the stack.
When a member wants to leave a group, it disconnects from the channel. This causes a DISCONNECT event to be sent down where it is caught by the GMS layer. The latter sends a unicast LEAVE request to the coordinator, which in turn removes the member from its local view and multicasts the new view.
When a SUSPECT event is received by the GMS layer, if the layer is the current coordinator, the member will be removed from the local view and a new view multicast to all members. Otherwise, the event is just dropped. In case the suspected member is the coordinator itself, the next member of the group in order takes over and multicasts a new view (excluding the old coordinator).